A377782 First-differences of A031218(n) = greatest number <= n that is 1 or a prime-power.

1, 1, 1, 1, 0, 2, 1, 1, 0, 2, 0, 2, 0, 0, 3, 1, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, 0, 2, 0, 2, 1, 0, 0, 0, 0, 5, 0, 0, 0, 4, 0, 2, 0, 0, 0, 4, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 3, 0, 0, 3, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 0, 2, 0, 0, 0, 0, 0

Offset: 1

Author

Gus Wiseman, Nov 16 2024

Keywords

• nonn

Comments

Note 1 is a power of a prime (A000961) but not a prime-power (A246655).

Crossrefs

Positions of 1 are A006549.

Positions of 0 are A080765 = A024619 - 1, complement A181062 = A000961 - 1.

Positions of 2 are A120432 (except initial terms).

Sorted positions of first appearances appear to include A167236 - 1.

Positions of terms > 1 are A373677.

The restriction to primes minus 1 is A377289.

Below, A (B) indicates that A is the first-differences of B:

- This sequence is A377782 (A031218), which has restriction to primes A065514 (A377781).

- The opposite is A377780 (A000015), restriction A377703 (A345531).

- For nonsquarefree we have A378036 (A378033), opposite A378039 (A120327).

- For squarefree we have A378085 (A112925), restriction A378038 (A070321).

A000040 lists the primes, differences A001223.

A000961 and A246655 list prime-powers, differences A057820.

A024619 lists the non-prime-powers, differences A375735, seconds A376599.

A361102 lists the non-powers of primes, differences A375708.

A378034 gives differences of A378032 (restriction of A378033).

Prime-powers between primes: A053607, A080101, A366833, A377057, A377286, A377287.

Cf. A053289, A343249, A375706, A377281, A377282.

Programs

Mathematica

Differences[Table[NestWhile[#-1&,n,#>1&&!PrimePowerQ[#]&],{n,100}]]