A379541 - OEIS

%I #7 Dec 25 2024 00:50:49

%S 2,5,11,17,19,29,37,41,43,53,59,67,71,73,83,89,97,101,103,107,109,131,

%T 137,139,149,151,157,163,173,179,181,191,193,197,199,211,223,227,229,

%U 233,239,257,263,269,271,277,281,293,307,311,313,317,331,347,349,353

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

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

%e After 13 the next prime power is 16, which is not prime, so 13 is not in the sequence.

%e After 19 the next prime power is 23, which is prime, so 19 is in the sequence.

%t nextpripow[n_]:=NestWhile[#1+1&,n+1,!PrimePowerQ[#1]&];

%t Select[Range[100],PrimeQ[#]&&PrimeQ[nextpripow[#]]&]

%Y For no primes we have A068315, positions A379156.

%Y Lesser of adjacent primes in A246655 (prime powers).

%Y The indices of these primes are A377286.

%Y For just one prime we have A379157, positions A379155.

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

%Y A000015 gives the least prime power >= n.

%Y A000040 lists the primes, differences A001223.

%Y A000961 lists the powers of primes, differences A057820.

%Y A031218 gives the greatest prime power <= n.

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

%Y A131605 finds perfect powers that are not prime powers.

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

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

%K nonn

%O 1,1

%A _Gus Wiseman_, Dec 24 2024