A379541 Prime numbers such that the next greatest prime power is also prime.

2, 5, 11, 17, 19, 29, 37, 41, 43, 53, 59, 67, 71, 73, 83, 89, 97, 101, 103, 107, 109, 131, 137, 139, 149, 151, 157, 163, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 257, 263, 269, 271, 277, 281, 293, 307, 311, 313, 317, 331, 347, 349, 353

Offset: 1

Author

Gus Wiseman, Dec 24 2024

Keywords

• nonn

Examples

			After 13 the next prime power is 16, which is not prime, so 13 is not in the sequence.
After 19 the next prime power is 23, which is prime, so 19 is in the sequence.
		

Crossrefs

For no primes we have A068315, positions A379156.

Lesser of adjacent primes in A246655 (prime powers).

The indices of these primes are A377286.

For just one prime we have A379157, positions A379155.

Positions in the prime powers are A379158 = positions of 2 in A366835.

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.

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

Cf. A025474, A067871, A080769, A178700, A274605, A345531, A377281, A377287, A378368.

Programs

Mathematica

nextpripow[n_]:=NestWhile[#1+1&,n+1,!PrimePowerQ[#1]&];
Select[Range[100],PrimeQ[#]&&PrimeQ[nextpripow[#]]&]

Formula

a(n) = A246655(A379158(n)).