A379156 Positions in A246655 (prime powers) of terms q such that there is no prime between q and the next prime power.

6, 14, 41, 359, 3589

Offset: 1

Author

Gus Wiseman, Dec 22 2024

Keywords

• nonn
• more

Comments

The powers of primes themselves are 8, 25, 121, 2187, 32761, ... (A068315).

Crossrefs

The prime powers themselves are A068315, for just one prime A379157.

For perfect powers instead of prime powers we have A274605.

Positions of 0 in A366835.

For just one prime we have A379155, for perfect powers A378368.

A000015 gives the least prime power >= n.

A000040 lists the primes, differences A001223.

A000961 lists the powers of primes, differences A057820.

A031218 gives the greatest prime power <= n.

A065514 gives the greatest prime power < prime(n), difference A377289.

A131605 finds perfect powers that are not prime powers.

A246655 lists the prime powers.

A366833 counts prime powers between primes, see A053607, A304521.

Cf. A025474, A046933, A067871, A080101, A080769, A175106, A178700, A345531, A377281, A377287, A377432, A377434.

Programs

Mathematica

v=Select[Range[100],PrimePowerQ];
Select[Range[Length[v]-1],FreeQ[Range[v[[#]],v[[#+1]]],_?PrimeQ]&]

Formula

A246655(a(n)) = A068315(n).