A378034 First-differences of A378032 (greatest number < prime(n) that is 1 or nonsquarefree).

0, 3, 0, 5, 3, 4, 2, 2, 8, 0, 8, 4, 0, 5, 7, 4, 4, 4, 4, 4, 4, 5, 7, 8, 4, 0, 4, 4, 4, 14, 2, 8, 0, 12, 2, 6, 6, 2, 8, 4, 4, 9, 3, 4, 2, 10, 12, 5, 3, 4, 4, 4, 10, 6, 5, 7, 2, 6, 4, 0, 12, 14, 2, 4, 4, 12, 8, 8, 4, 4, 4, 8, 8, 6, 2, 8, 8, 4, 8, 8, 4, 8, 4, 4

Offset: 1

Author

Gus Wiseman, Nov 18 2024

Keywords

• nonn

Crossrefs

Positions of 0 are A068361.

The opposite for prime-powers is A377703, differences of A345531.

For prime-powers we have A377781, differences of A065514.

The opposite is A377784, differences of A377783 (union A378040).

First-differences of A378032.

Restriction of A378036, differences of A378033.

The opposite for squarefree numbers is A378037, differences of A112926.

For squarefree numbers we have A378038, differences of A112925.

The unrestricted opposite is A378039, differences of A120327 (union A162966).

A000040 lists the primes, differences A001223, seconds A036263.

A005117 lists the squarefree numbers.

A013929 lists the nonsquarefree numbers, differences A078147, seconds A376593.

A061398 counts squarefree numbers between primes (sums A337030), zeros A068360.

A061399 counts nonsquarefree numbers between primes (sums A378086), zeros A068361.

A070321 gives the greatest squarefree number up to n.

A377046 encodes k-differences of nonsquarefree numbers, zeros A377050.

Cf. A053797, A053806, A072284, A065890, A224363, A377430, A377431.

Cf. A377047, A377048, A377049, A378082, A378083, A378084.

Programs

Mathematica

Differences[Table[NestWhile[#-1&,Prime[n],#>1&&SquareFreeQ[#]&],{n,100}]]

Formula

a(n) = A378036(prime(n)).