A068315 For numbers k such that A025474(k) > 1 and A025474(k+1) > 1, sequence gives A000961(k).

8, 25, 121, 2187, 32761

Offset: 1

Author

Naohiro Nomoto, Mar 08 2002

Keywords

• nonn
• hard
• more

Comments

Equivalently, prime powers (either A000961 or A246655) q such that q and the next prime power are both composite numbers. - Paolo Xausa, Oct 25 2023

Examples

			The interval (121,122,123,124,125) contains no primes, so 121 is in the sequence. - _Gus Wiseman_, Dec 24 2024
		

Crossrefs

Bisection of A068435.

For perfect powers instead of prime powers we have A116086, indices A274605.

The position of a(k) in the prime powers A246655 is A379156(k).

For just one prime we have A379157, indices A379155.

A000015 gives the least prime power >= n.

A000040 lists the primes, differences A001223.

A031218 gives the greatest prime power <= n.

A046933 gives run-lengths of composites between primes.

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

A246655 lists the prime powers, differences A057820.

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

A366835 counts primes between prime powers.

Cf. A025474, A067871, A080101, A080769, A175106, A345531, A377281, A377287, A378368.

Programs

Mathematica

With[{upto=33000},Map[First,Select[Partition[Select[Range[upto],PrimePowerQ],2,1],NoneTrue[#,PrimeQ]&]]] (* Paolo Xausa, Oct 25 2023 *)

Formula

a(n) = A246655(A379156(n)). - Gus Wiseman, Dec 24 2024

Extensions

Definition corrected by Jinyuan Wang, Sep 05 2020