This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A376597 #5 Oct 05 2024 14:00:26 %S A376597 1,2,3,6,8,14,15,16,27,32,50,61,67,72,85,92,93,124,129,132,136,141, %T A376597 185,190,211,214,221,226,268,292,301,302,322,374,394,423,456,463,502, %U A376597 503,547,559,560,593,604,640,646,663,671,675,710,726,727,746,754,755 %N A376597 Inflection and undulation points in the sequence of prime-powers inclusive (A000961). %C A376597 These are points at which the second differences (A376596) are zero. %C A376597 Inclusive means 1 is a prime-power. For the exclusive version, subtract 1 and shift left. %H A376597 Gus Wiseman, <a href="/A376597/a376597.png">Inflection and undulation points in the prime-powers inclusive</a>. %e A376597 The prime-powers inclusive (A000961) are: %e A376597 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, ... %e A376597 with first differences (A057820): %e A376597 1, 1, 1, 1, 2, 1, 1, 2, 2, 3, 1, 2, 4, 2, 2, 2, 2, 1, 5, 4, 2, 4, 2, 4, 6, 2, ... %e A376597 with first differences (A376596): %e A376597 0, 0, 0, 1, -1, 0, 1, 0, 1, -2, 1, 2, -2, 0, 0, 0, -1, 4, -1, -2, 2, -2, 2, 2, ... %e A376597 with zeros (A376597) at: %e A376597 1, 2, 3, 6, 8, 14, 15, 16, 27, 32, 50, 61, 67, 72, 85, 92, 93, 124, 129, 132, ... %t A376597 Join@@Position[Differences[Select[Range[1000],#==1||PrimePowerQ[#]&],2],0] %Y A376597 The first differences were A057820, see also A053707, A376340. %Y A376597 These are the zeros of A376596 (sorted firsts A376653, exclusive A376654). %Y A376597 The complement is A376598. %Y A376597 A000961 lists prime-powers inclusive, exclusive A246655. %Y A376597 A001597 lists perfect-powers, complement A007916. %Y A376597 A023893 and A023894 count integer partitions into prime-powers, factorizations A000688. %Y A376597 A064113 lists positions of adjacent equal prime gaps. %Y A376597 For prime-powers inclusive: A057820 (first differences), A376596 (second differences), A376598 (nonzero curvature). %Y A376597 For second differences: A036263 (prime), A073445 (composite), A376559 (perfect-power), A376562 (non-perfect-power), A376590 (squarefree), A376593 (nonsquarefree), A376599 (non-prime-power). %Y A376597 Cf. A025475, A053707, A069623, A093555, A174965, A361102, A376653, A376654. %K A376597 nonn %O A376597 1,2 %A A376597 _Gus Wiseman_, Oct 05 2024