THE WEIGHT × LEVEL + JUMP ATLAS

Integer sequences, seen through a shared lens.

Explore how arithmetic structure takes shape across 200 integer sequences: natural numbers, primes, figurate numbers, digit patterns and more. The decomposition a(n) = k(n)L(n) + d(n) connects each term’s next gap, or jump, with its weight and level.

200 sequences40,000,000 computed pointsInteractive 2D & 3D graphs

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200 sequences

Weight–level previews · first 25,000 plotted terms · equal log scalesWeight (k ≤ L)Level (k > L)

Weight–level projection of Natural numbers; natural logarithms on equal scales

Natural numbers

Weight–level projection of Odd exponent-bit parity; natural logarithms on equal scales

Odd exponent-bit parity

Weight–level projection of Nonsquares; natural logarithms on equal scales

Nonsquares

Weight–level projection of Prime numbers; natural logarithms on equal scales

Prime numbers

Weight–level projection of Odious numbers; natural logarithms on equal scales

Odious numbers

Weight–level projection of Floor of n to the 3/2; natural logarithms on equal scales

Floor of n to the 3/2

Weight–level projection of Triangular numbers plus n; natural logarithms on equal scales

Triangular numbers plus n

Weight–level projection of Central polygonal numbers; natural logarithms on equal scales

Central polygonal numbers

Weight–level projection of Lower Wythoff sequence; natural logarithms on equal scales

Lower Wythoff sequence

Weight–level projection of Triangular numbers; natural logarithms on equal scales

Triangular numbers

Weight–level projection of Square numbers; natural logarithms on equal scales

Square numbers

Weight–level projection of Pentagonal numbers; natural logarithms on equal scales

Pentagonal numbers

Weight–level projection of Sums of three squares; natural logarithms on equal scales

Sums of three squares

Weight–level projection of Even exponent-bit parity; natural logarithms on equal scales

Even exponent-bit parity

Weight–level projection of Hexagonal numbers; natural logarithms on equal scales

Hexagonal numbers

Weight–level projection of Sums of two positive squares; natural logarithms on equal scales

Sums of two positive squares

Weight–level projection of Require two positive squares; natural logarithms on equal scales

Require two positive squares

Weight–level projection of Squarefree composites and 1; natural logarithms on equal scales

Squarefree composites and 1

Weight–level projection of Cumulative binary digit sum; natural logarithms on equal scales

Cumulative binary digit sum

Weight–level projection of Prime powers; natural logarithms on equal scales

Prime powers

Weight–level projection of At least three prime factors; natural logarithms on equal scales

At least three prime factors

Weight–level projection of Sums of consecutive primes; natural logarithms on equal scales

Sums of consecutive primes

Weight–level projection of Twin primes; natural logarithms on equal scales

Twin primes

Weight–level projection of Semiprimes; natural logarithms on equal scales

Semiprimes

Weight–level projection of Lesser twin primes; natural logarithms on equal scales

Lesser twin primes

Weight–level projection of Sums of two squares; natural logarithms on equal scales

Sums of two squares

Weight–level projection of Not divisible by 3; natural logarithms on equal scales

Not divisible by 3

Weight–level projection of Primes and twice primes; natural logarithms on equal scales

Primes and twice primes

Weight–level projection of Triangle packing numbers; natural logarithms on equal scales

Triangle packing numbers

Weight–level projection of Centered square numbers; natural logarithms on equal scales

Centered square numbers

Weight–level projection of Binary-insertion sorting numbers; natural logarithms on equal scales

Binary-insertion sorting numbers

Weight–level projection of Beatty: 2 + √2; natural logarithms on equal scales

Beatty: 2 + √2

Weight–level projection of Evil numbers; natural logarithms on equal scales

Evil numbers

Weight–level projection of Residues 2, 4, 8, 16 modulo 20; natural logarithms on equal scales

Residues 2, 4, 8, 16 modulo 20

Weight–level projection of Decimal palindromes; natural logarithms on equal scales

Decimal palindromes

Weight–level projection of Primes ≡ 1 (mod 4); natural logarithms on equal scales

Primes ≡ 1 (mod 4)

Weight–level projection of Primes ≡ 3 (mod 4); natural logarithms on equal scales

Primes ≡ 3 (mod 4)

Weight–level projection of Pronic numbers; natural logarithms on equal scales

Pronic numbers

Weight–level projection of Primes ≡ 1 (mod 6); natural logarithms on equal scales

Primes ≡ 1 (mod 6)

Weight–level projection of Squares plus one; natural logarithms on equal scales

Squares plus one

Weight–level projection of Quarter-squares; natural logarithms on equal scales

Quarter-squares

Weight–level projection of Composite numbers; natural logarithms on equal scales

Composite numbers

Weight–level projection of Twin-prime centers / 6; natural logarithms on equal scales

Twin-prime centers / 6

Weight–level projection of Decimal self numbers; natural logarithms on equal scales

Decimal self numbers

Weight–level projection of Loeschian numbers; natural logarithms on equal scales

Loeschian numbers

Weight–level projection of Cyclic numbers; natural logarithms on equal scales

Cyclic numbers

Weight–level projection of Beatty: (1 + √3)/2; natural logarithms on equal scales

Beatty: (1 + √3)/2

Weight–level projection of Beatty: 2 + √3; natural logarithms on equal scales

Beatty: 2 + √3

Weight–level projection of Integer divisor averages; natural logarithms on equal scales

Integer divisor averages

Weight–level projection of Primes ≡ 5 or 7 (mod 8); natural logarithms on equal scales

Primes ≡ 5 or 7 (mod 8)

Weight–level projection of Primes ≡ 2 or 3 (mod 5); natural logarithms on equal scales

Primes ≡ 2 or 3 (mod 5)

Weight–level projection of Binary numbers without 111; natural logarithms on equal scales

Binary numbers without 111

Weight–level projection of Binary numbers without 000; natural logarithms on equal scales

Binary numbers without 000

Weight–level projection of Take one, skip one, take two…; natural logarithms on equal scales

Take one, skip one, take two…

Weight–level projection of Skip one, take one, skip two…; natural logarithms on equal scales

Skip one, take one, skip two…

Weight–level projection of Require four squares; natural logarithms on equal scales

Require four squares

Weight–level projection of Sums of two distinct positive squares; natural logarithms on equal scales

Sums of two distinct positive squares

Weight–level projection of Prime factors ≡ 1 (mod 3); natural logarithms on equal scales

Prime factors ≡ 1 (mod 3)

Weight–level projection of Prime factors ≡ 1 (mod 4); natural logarithms on equal scales

Prime factors ≡ 1 (mod 4)

Weight–level projection of Prime factors ≡ 3 (mod 4); natural logarithms on equal scales

Prime factors ≡ 3 (mod 4)

Weight–level projection of Binary numbers without 101; natural logarithms on equal scales

Binary numbers without 101

Weight–level projection of Binary numbers without 110; natural logarithms on equal scales

Binary numbers without 110

Weight–level projection of Binary numbers without 011; natural logarithms on equal scales

Binary numbers without 011

Weight–level projection of Binary numbers without 001; natural logarithms on equal scales

Binary numbers without 001

Weight–level projection of Binary numbers without 010; natural logarithms on equal scales

Binary numbers without 010

Weight–level projection of Binary numbers containing 11; natural logarithms on equal scales

Binary numbers containing 11

Weight–level projection of Prime-producing indices: 4n + 1; natural logarithms on equal scales

Prime-producing indices: 4n + 1

Weight–level projection of Deficient numbers; natural logarithms on equal scales

Deficient numbers

Weight–level projection of Abundant numbers; natural logarithms on equal scales

Abundant numbers

Weight–level projection of Squarefree numbers; natural logarithms on equal scales

Squarefree numbers

Weight–level projection of Practical numbers; natural logarithms on equal scales

Practical numbers

Weight–level projection of Harshad numbers; natural logarithms on equal scales

Harshad numbers

Weight–level projection of Consecutive composite pairs; natural logarithms on equal scales

Consecutive composite pairs

Weight–level projection of Sophie Germain primes; natural logarithms on equal scales

Sophie Germain primes

Weight–level projection of Safe primes; natural logarithms on equal scales

Safe primes

Weight–level projection of Odd numbers; natural logarithms on equal scales

Odd numbers

Weight–level projection of Even numbers; natural logarithms on equal scales

Even numbers

Weight–level projection of Primes minus one; natural logarithms on equal scales

Primes minus one

Weight–level projection of Even binary parity above the last bit; natural logarithms on equal scales

Even binary parity above the last bit

Weight–level projection of Floor-root divisibility numbers; natural logarithms on equal scales

Floor-root divisibility numbers

Weight–level projection of Prime-indexed primes; natural logarithms on equal scales

Prime-indexed primes

Weight–level projection of Greater twin primes; natural logarithms on equal scales

Greater twin primes

Weight–level projection of Emirps; natural logarithms on equal scales

Emirps

Weight–level projection of Smith numbers; natural logarithms on equal scales

Smith numbers

Weight–level projection of Squarefree semiprimes; natural logarithms on equal scales

Squarefree semiprimes

Weight–level projection of Binary palindromes; natural logarithms on equal scales

Binary palindromes

Weight–level projection of Products of three distinct primes; natural logarithms on equal scales

Products of three distinct primes

Weight–level projection of Numbers coprime to 6; natural logarithms on equal scales

Numbers coprime to 6

Weight–level projection of Noncubes; natural logarithms on equal scales

Noncubes

Weight–level projection of Isolated primes; natural logarithms on equal scales

Isolated primes

Weight–level projection of Primes ≡ 5 (mod 6); natural logarithms on equal scales

Primes ≡ 5 (mod 6)

Weight–level projection of Take one, skip two; natural logarithms on equal scales

Take one, skip two

Weight–level projection of Digit-sum orbit from 5; natural logarithms on equal scales

Digit-sum orbit from 5

Weight–level projection of Two-square sums in multiple ways; natural logarithms on equal scales

Two-square sums in multiple ways

Weight–level projection of Happy numbers; natural logarithms on equal scales

Happy numbers

Weight–level projection of Numbers containing an odd digit; natural logarithms on equal scales

Numbers containing an odd digit

Weight–level projection of 11-rough numbers; natural logarithms on equal scales

11-rough numbers

Weight–level projection of 13-rough numbers; natural logarithms on equal scales

13-rough numbers

Weight–level projection of 17-rough numbers; natural logarithms on equal scales

17-rough numbers

Weight–level projection of Primitive Pythagorean hypotenuses; natural logarithms on equal scales

Primitive Pythagorean hypotenuses

Weight–level projection of Numbers ≡ 0 or 1 (mod 5); natural logarithms on equal scales

Numbers ≡ 0 or 1 (mod 5)

Weight–level projection of Primes plus one; natural logarithms on equal scales

Primes plus one

Weight–level projection of Binary self numbers; natural logarithms on equal scales

Binary self numbers

Weight–level projection of Base-4 self numbers; natural logarithms on equal scales

Base-4 self numbers

Weight–level projection of Distinct decimal digits; natural logarithms on equal scales

Distinct decimal digits

Weight–level projection of Numbers containing 1; natural logarithms on equal scales

Numbers containing 1

Weight–level projection of Numbers containing 2; natural logarithms on equal scales

Numbers containing 2

Weight–level projection of Numbers containing 3; natural logarithms on equal scales

Numbers containing 3

Weight–level projection of Numbers containing 9; natural logarithms on equal scales

Numbers containing 9

Weight–level projection of Numbers containing 0; natural logarithms on equal scales

Numbers containing 0

Weight–level projection of Cumulative distinct prime factors; natural logarithms on equal scales

Cumulative distinct prime factors

Weight–level projection of Odd nonprimes; natural logarithms on equal scales

Odd nonprimes

Weight–level projection of Ternary palindromes; natural logarithms on equal scales

Ternary palindromes

Weight–level projection of Palindromes in base 4; natural logarithms on equal scales

Palindromes in base 4

Weight–level projection of Odd digits only; natural logarithms on equal scales

Odd digits only

Weight–level projection of Even digits only; natural logarithms on equal scales

Even digits only

Weight–level projection of Exactly five binary ones; natural logarithms on equal scales

Exactly five binary ones

Weight–level projection of Twin-prime centers; natural logarithms on equal scales

Twin-prime centers

Weight–level projection of 3-almost primes; natural logarithms on equal scales

3-almost primes

Weight–level projection of 4-almost primes; natural logarithms on equal scales

4-almost primes

Weight–level projection of 5-almost primes; natural logarithms on equal scales

5-almost primes

Weight–level projection of Prime plus its index; natural logarithms on equal scales

Prime plus its index

Weight–level projection of Odd power-of-two residues; natural logarithms on equal scales

Odd power-of-two residues

Weight–level projection of Digit-sum orbit from 3; natural logarithms on equal scales

Digit-sum orbit from 3

Weight–level projection of Digit-sum orbit from 9; natural logarithms on equal scales

Digit-sum orbit from 9

Weight–level projection of Not two nonzero squares; natural logarithms on equal scales

Not two nonzero squares

Weight–level projection of Hoax numbers; natural logarithms on equal scales

Hoax numbers

Weight–level projection of Square plus seven times a square; natural logarithms on equal scales

Square plus seven times a square

Weight–level projection of Sums of two triangular numbers; natural logarithms on equal scales

Sums of two triangular numbers

Weight–level projection of Not two triangular numbers; natural logarithms on equal scales

Not two triangular numbers

Weight–level projection of Not two squares; natural logarithms on equal scales

Not two squares

Weight–level projection of Square plus cube; natural logarithms on equal scales

Square plus cube

Weight–level projection of Prime factors of factorials; natural logarithms on equal scales

Prime factors of factorials

Weight–level projection of Beatty: √5; natural logarithms on equal scales

Beatty: √5

Weight–level projection of Beatty: √7; natural logarithms on equal scales

Beatty: √7

Weight–level projection of Beatty: √8; natural logarithms on equal scales

Beatty: √8

Weight–level projection of Divisor sum at least 3n; natural logarithms on equal scales

Divisor sum at least 3n

Weight–level projection of Lesser cousin primes; natural logarithms on equal scales

Lesser cousin primes

Weight–level projection of Lesser sexy primes; natural logarithms on equal scales

Lesser sexy primes

Weight–level projection of Base-4 numbers without 0; natural logarithms on equal scales

Base-4 numbers without 0

Weight–level projection of Base-5 numbers without 3; natural logarithms on equal scales

Base-5 numbers without 3

Weight–level projection of Not prime powers; natural logarithms on equal scales

Not prime powers

Weight–level projection of Means of consecutive odd primes; natural logarithms on equal scales

Means of consecutive odd primes

Weight–level projection of Prime-producing indices: 5n + 1; natural logarithms on equal scales

Prime-producing indices: 5n + 1

Weight–level projection of Prime-producing indices: 6n − 1; natural logarithms on equal scales

Prime-producing indices: 6n − 1

Weight–level projection of Unique positive two-square sums; natural logarithms on equal scales

Unique positive two-square sums

Weight–level projection of Primes without a twin below; natural logarithms on equal scales

Primes without a twin below

Weight–level projection of Lower Wythoff sequence plus one; natural logarithms on equal scales

Lower Wythoff sequence plus one

Weight–level projection of Odd total prime-factor count; natural logarithms on equal scales

Odd total prime-factor count

Weight–level projection of Odious primes; natural logarithms on equal scales

Odious primes

Weight–level projection of Evil primes; natural logarithms on equal scales

Evil primes

Weight–level projection of Even total prime-factor count; natural logarithms on equal scales

Even total prime-factor count

Weight–level projection of Curved decimal digits; natural logarithms on equal scales

Curved decimal digits

Weight–level projection of Prime decimal digital root; natural logarithms on equal scales

Prime decimal digital root

Weight–level projection of Decimal nonpalindromes; natural logarithms on equal scales

Decimal nonpalindromes

Weight–level projection of Palindromes in base 8; natural logarithms on equal scales

Palindromes in base 8

Weight–level projection of Palindromes in base 5; natural logarithms on equal scales

Palindromes in base 5

Weight–level projection of Palindromes in base 6; natural logarithms on equal scales

Palindromes in base 6

Weight–level projection of Palindromes in base 7; natural logarithms on equal scales

Palindromes in base 7

Weight–level projection of Palindromes in base 9; natural logarithms on equal scales

Palindromes in base 9

Weight–level projection of Alternating decimal digit parity; natural logarithms on equal scales

Alternating decimal digit parity

Weight–level projection of Even numbers with alternating digit parity; natural logarithms on equal scales

Even numbers with alternating digit parity

Weight–level projection of Unhappy numbers; natural logarithms on equal scales

Unhappy numbers

Weight–level projection of Odd-indexed primes; natural logarithms on equal scales

Odd-indexed primes

Weight–level projection of Balanced binary digits; natural logarithms on equal scales

Balanced binary digits

Weight–level projection of Lower primes of consecutive gap 6; natural logarithms on equal scales

Lower primes of consecutive gap 6

Weight–level projection of Upper primes of consecutive gap 6; natural logarithms on equal scales

Upper primes of consecutive gap 6

Weight–level projection of Ternary numbers without 0; natural logarithms on equal scales

Ternary numbers without 0

Weight–level projection of Primes represented by x² + 2y²; natural logarithms on equal scales

Primes represented by x² + 2y²

Weight–level projection of Numbers with a primitive root; natural logarithms on equal scales

Numbers with a primitive root

Weight–level projection of Numbers without a primitive root; natural logarithms on equal scales

Numbers without a primitive root

Weight–level projection of Refactorable numbers; natural logarithms on equal scales

Refactorable numbers

Weight–level projection of Not Loeschian numbers; natural logarithms on equal scales

Not Loeschian numbers

Weight–level projection of Multiplicative digital root zero; natural logarithms on equal scales

Multiplicative digital root zero

Weight–level projection of Unitary abundant numbers; natural logarithms on equal scales

Unitary abundant numbers

Weight–level projection of Divisible by the last digit; natural logarithms on equal scales

Divisible by the last digit

Weight–level projection of Divisible by the first digit; natural logarithms on equal scales

Divisible by the first digit

Weight–level projection of Divisible by every digit; natural logarithms on equal scales

Divisible by every digit

Weight–level projection of Happy primes; natural logarithms on equal scales

Happy primes

Weight–level projection of Equal even and odd digit sums; natural logarithms on equal scales

Equal even and odd digit sums

Weight–level projection of Divisor count appears as a digit; natural logarithms on equal scales

Divisor count appears as a digit

Weight–level projection of Power-of-two divisor counts; natural logarithms on equal scales

Power-of-two divisor counts

Weight–level projection of At most three prime factors; natural logarithms on equal scales

At most three prime factors

Weight–level projection of Equal digit sums in bases 2 and 3; natural logarithms on equal scales

Equal digit sums in bases 2 and 3

Weight–level projection of Equal digit sums in bases 2 and 10; natural logarithms on equal scales

Equal digit sums in bases 2 and 10

Weight–level projection of Zeroless primes; natural logarithms on equal scales

Zeroless primes

Weight–level projection of Divisible by at least one digit; natural logarithms on equal scales

Divisible by at least one digit

Weight–level projection of Divisible by none of the digits; natural logarithms on equal scales

Divisible by none of the digits

Weight–level projection of Primes with quadratic residue 2; natural logarithms on equal scales

Primes with quadratic residue 2

Weight–level projection of Balanced ones and twos in base 4; natural logarithms on equal scales

Balanced ones and twos in base 4

Weight–level projection of Squarefree numbers ≡ 1 (mod 4); natural logarithms on equal scales

Squarefree numbers ≡ 1 (mod 4)

Weight–level projection of Even squarefree numbers; natural logarithms on equal scales

Even squarefree numbers

Weight–level projection of Squarefree numbers ≡ 3 (mod 4); natural logarithms on equal scales

Squarefree numbers ≡ 3 (mod 4)

Weight–level projection of Distinct adjacent decimal digits; natural logarithms on equal scales

Distinct adjacent decimal digits

Weight–level projection of Exactly one decimal zero; natural logarithms on equal scales

Exactly one decimal zero

Weight–level projection of Primes ≡ 1 or 4 (mod 5); natural logarithms on equal scales

Primes ≡ 1 or 4 (mod 5)

Weight–level projection of Largest-digit orbit; natural logarithms on equal scales

Largest-digit orbit

Weight–level projection of Strong primes; natural logarithms on equal scales

Strong primes

Weight–level projection of Weak primes; natural logarithms on equal scales

Weak primes

Weight–level projection of Zeroless numbers; natural logarithms on equal scales

Zeroless numbers