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

8, 25, 121, 2187, 32761

Offset

1,1

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

Links

Table of n, a(n) for n=1..5.

Formula

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

Example

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

Mathematica

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

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.

Sequence in context: A139026 A135942 A181207 * A069586 A253237 A275151

Adjacent sequences: A068312 A068313 A068314 * A068316 A068317 A068318

Keyword

nonn,hard,more

Author

Naohiro Nomoto, Mar 08 2002

Extensions

Definition corrected by Jinyuan Wang, Sep 05 2020

Status

approved