A377780 First differences of A000015 (smallest prime-power >= n).

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

Offset: 1

Author

Gus Wiseman, Nov 13 2024

Keywords

• nonn

Crossrefs

First differences of A000015, restriction to primes A345531.

The opposite is A377782, restriction to primes A377781, differences of A065514.

For squarefree instead of prime-power see A067535, A112925, A112926, A120327.

A000040 lists the primes, differences A001223.

A000961 and A246655 list the prime-powers, differences A057820.

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

A080101 counts prime-powers between primes (exclusive).

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

A366833 counts prime-powers between primes.

Cf. A001597, A007916, A007949, A031218, A053289, A053607, A343249, A343250, A377282, A377289, A377468.

Programs

Mathematica

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