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A375713 Indices of consecutive non-prime-powers (A361102) differing by 1. Numbers k such that the k-th and (k+1)-th non-prime-powers differ by just one.

%I A375713 #8 Sep 08 2024 19:26:42
%S A375713 5,8,9,15,16,17,19,20,23,24,27,28,30,31,32,33,36,38,40,41,44,45,46,47,
%T A375713 51,52,53,54,56,57,58,59,60,61,63,64,67,68,71,72,74,75,76,77,78,79,81,
%U A375713 82,85,87,88,89,90,93,94,95,96,97,98,99,100,103,104,105,106
%N A375713 Indices of consecutive non-prime-powers (A361102) differing by 1. Numbers k such that the k-th and (k+1)-th non-prime-powers differ by just one.
%F A375713 A361102(k+1) - A361102(k) = 1.
%e A375713 The initial non-prime-powers are 1, 6, 10, 12, 14, 15, 18, 20, 21, which first increase by one after the fifth and eighth terms.
%t A375713 Join@@Position[Differences[Select[Range[100],!PrimePowerQ[#]&]],1]
%Y A375713 The inclusive version is a(n) - 1.
%Y A375713 For prime-powers inclusive (A000961) we have A375734, differences A373671.
%Y A375713 For nonprime numbers (A002808) we have A375926, differences A373403.
%Y A375713 For prime-powers exclusive (A246655) we have A375734(n+1) + 1.
%Y A375713 First differences are A373672.
%Y A375713 Positions of 1's in A375708.
%Y A375713 For non-perfect-powers we have A375740.
%Y A375713 Prime-powers inclusive:
%Y A375713 - terms: A000961
%Y A375713 - differences: A057820
%Y A375713 - runs: A373675, A373673, A373674, A174965
%Y A375713 - antiruns: A373576, A120430, A006549, A373671
%Y A375713 Non-prime-powers inclusive:
%Y A375713 - terms: A361102
%Y A375713 - differences: A375708
%Y A375713 - runs: A373678, A373676, A373677, A110969
%Y A375713 - antiruns: A373679, A373575, A255346, A373672
%Y A375713 A000040 lists all of the primes, differences A001223.
%Y A375713 A007916 lists non-perfect-powers, differences A375706.
%Y A375713 Cf. A046933, A053289, A073783, A093555, A176246, A251092, A375714.
%K A375713 nonn
%O A375713 1,1
%A A375713 _Gus Wiseman_, Sep 02 2024