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

%I A379158 #7 Dec 25 2024 00:50:46
%S A379158 1,4,8,11,12,16,19,20,21,24,25,28,29,30,33,34,35,36,37,38,39,45,46,47,
%T A379158 48,49,50,51,54,55,56,57,58,59,60,61,62,63,64,65,66,71,72,73,74,75,76,
%U A379158 79,80,81,82,83,84,87,88,89,92,93,94,95,96,97,98,99,100
%N A379158 Numbers m such that the consecutive prime powers A246655(m) and A246655(m+1) are both prime.
%C A379158 Also positions of 2 in A366835.
%F A379158 A246655(a(n)) = A379541(n).
%e A379158 The 4th and 5th prime powers are 5 and 7, which are both prime, so 4 is in the sequence.
%e A379158 The 12th and 13th prime powers are 19 and 23, which are both prime, so 12 is in the sequence.
%t A379158 v=Select[Range[100],PrimePowerQ];
%t A379158 Select[Range[Length[v]-1],PrimeQ[v[[#]]]&&PrimeQ[v[[#+1]]]&]
%Y A379158 Positions of adjacent primes in A246655 (prime powers).
%Y A379158 Positions of 2 in A366835.
%Y A379158 For just one prime we have A379155, positions of prime powers in A379157.
%Y A379158 For no primes we have A379156, positions of prime powers in A068315.
%Y A379158 The primes powers themselves are A379541.
%Y A379158 A000015 gives the least prime power >= n.
%Y A379158 A000040 lists the primes, differences A001223.
%Y A379158 A000961 lists the powers of primes, differences A057820.
%Y A379158 A031218 gives the greatest prime power <= n.
%Y A379158 A065514 gives the greatest prime power < prime(n), difference A377289.
%Y A379158 A131605 finds perfect powers that are not prime powers.
%Y A379158 A366833 counts prime powers between primes, see A053607, A304521.
%Y A379158 Cf. A025474, A067871, A080769, A178700, A274605, A345531, A377281, A377287, A378368.
%K A379158 nonn
%O A379158 1,2
%A A379158 _Gus Wiseman_, Dec 23 2024