cp's OEIS Frontend

A379157 Prime powers p such that the interval from p to the next prime power contains a unique prime number.

%I A379157 #8 Dec 23 2024 09:56:22
%S A379157 3,4,7,9,13,16,23,27,31,32,47,49,61,64,79,81,113,125,127,128,167,169,
%T A379157 241,243,251,256,283,289,337,343,359,361,509,512,523,529,619,625,727,
%U A379157 729,839,841,953,961,1021,1024,1327,1331,1367,1369,1669,1681,1847,1849
%N A379157 Prime powers p such that the interval from p to the next prime power contains a unique prime number.
%F A379157 a(n) = A246655(A379155(n)).
%e A379157 The next prime power after 32 is 37, with interval (32,33,34,35,36,37) containing just one prime 37, so 32 is in the sequence.
%t A379157 v=Select[Range[100],PrimePowerQ]
%t A379157 nextpripow[n_]:=NestWhile[#+1&,n+1,!PrimePowerQ[#]&]
%t A379157 Select[v,Length[Select[Range[#,nextpripow[#]],PrimeQ]]==1&]
%Y A379157 For no primes we have A068315/A379156, for perfect powers A116086/A274605.
%Y A379157 The previous instead of next prime power we have A175106.
%Y A379157 For perfect powers instead of prime powers we have A378355.
%Y A379157 The positions of these prime powers (in A246655) are A379155.
%Y A379157 A000015 gives the least prime power >= n.
%Y A379157 A000040 lists the primes, differences A001223.
%Y A379157 A000961 lists the powers of primes, differences A057820.
%Y A379157 A031218 gives the greatest prime power <= n.
%Y A379157 A065514 gives the greatest prime power < prime(n), difference A377289.
%Y A379157 A246655 lists the prime powers.
%Y A379157 A366833 counts prime powers between primes, see A053607, A304521.
%Y A379157 A366835 counts primes between prime powers, for perfect powers A080769.
%Y A379157 Cf. A046933, A067871, A080101, A178700, A345531, A377281, A377287, A377434, A378374.
%K A379157 nonn
%O A379157 1,1
%A A379157 _Gus Wiseman_, Dec 22 2024