cp's OEIS Frontend

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

%I A379541 #7 Dec 25 2024 00:50:49
%S A379541 2,5,11,17,19,29,37,41,43,53,59,67,71,73,83,89,97,101,103,107,109,131,
%T A379541 137,139,149,151,157,163,173,179,181,191,193,197,199,211,223,227,229,
%U A379541 233,239,257,263,269,271,277,281,293,307,311,313,317,331,347,349,353
%N A379541 Prime numbers such that the next greatest prime power is also prime.
%F A379541 a(n) = A246655(A379158(n)).
%e A379541 After 13 the next prime power is 16, which is not prime, so 13 is not in the sequence.
%e A379541 After 19 the next prime power is 23, which is prime, so 19 is in the sequence.
%t A379541 nextpripow[n_]:=NestWhile[#1+1&,n+1,!PrimePowerQ[#1]&];
%t A379541 Select[Range[100],PrimeQ[#]&&PrimeQ[nextpripow[#]]&]
%Y A379541 For no primes we have A068315, positions A379156.
%Y A379541 Lesser of adjacent primes in A246655 (prime powers).
%Y A379541 The indices of these primes are A377286.
%Y A379541 For just one prime we have A379157, positions A379155.
%Y A379541 Positions in the prime powers are A379158 = positions of 2 in A366835.
%Y A379541 A000015 gives the least prime power >= n.
%Y A379541 A000040 lists the primes, differences A001223.
%Y A379541 A000961 lists the powers of primes, differences A057820.
%Y A379541 A031218 gives the greatest prime power <= n.
%Y A379541 A065514 gives the greatest prime power < prime(n), difference A377289.
%Y A379541 A131605 finds perfect powers that are not prime powers.
%Y A379541 A366833 counts prime powers between primes, see A053607, A304521.
%Y A379541 Cf. A025474, A067871, A080769, A178700, A274605, A345531, A377281, A377287, A378368.
%K A379541 nonn
%O A379541 1,1
%A A379541 _Gus Wiseman_, Dec 24 2024