A379158 Numbers m such that the consecutive prime powers A246655(m) and A246655(m+1) are both prime.

1, 4, 8, 11, 12, 16, 19, 20, 21, 24, 25, 28, 29, 30, 33, 34, 35, 36, 37, 38, 39, 45, 46, 47, 48, 49, 50, 51, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 71, 72, 73, 74, 75, 76, 79, 80, 81, 82, 83, 84, 87, 88, 89, 92, 93, 94, 95, 96, 97, 98, 99, 100

Offset: 1

Author

Gus Wiseman, Dec 23 2024

Keywords

• nonn

Comments

Also positions of 2 in A366835.

Examples

			The 4th and 5th prime powers are 5 and 7, which are both prime, so 4 is in the sequence.
The 12th and 13th prime powers are 19 and 23, which are both prime, so 12 is in the sequence.
		

Crossrefs

Positions of adjacent primes in A246655 (prime powers).

Positions of 2 in A366835.

For just one prime we have A379155, positions of prime powers in A379157.

For no primes we have A379156, positions of prime powers in A068315.

The primes powers themselves are A379541.

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

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

Formula

A246655(a(n)) = A379541(n).