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 A376602 #11 Oct 07 2024 09:08:07 %S A376602 1,3,5,7,9,11,14,15,16,18,20,21,22,25,27,29,32,33,34,37,38,39,41,43, %T A376602 44,45,48,50,52,53,54,57,60,61,62,65,66,67,68,69,72,74,76,78,80,83,84, %U A376602 85,86,87,88,89,90,91,92,93,96,99,100,101,103,105,106,107,108 %N A376602 Inflection and undulation points in the sequence of composite numbers (A002808). %C A376602 These are points at which the second differences (A073445) are zero. %H A376602 Wikipedia, <a href="https://en.wikipedia.org/wiki/Inflection_point">Inflection point</a> %H A376602 Gus Wiseman, <a href="/A376602/a376602.png">Inflection and undulation points in the sequence of composite numbers</a>. %e A376602 The composite numbers (A002808) are: %e A376602 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, ... %e A376602 with first differences (A073783): %e A376602 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, ... %e A376602 with first differences (A073445): %e A376602 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, -1, 0, ... %e A376602 with zeros at (A376602): %e A376602 1, 3, 5, 7, 9, 11, 14, 15, 16, 18, 20, 21, 22, 25, 27, 29, 32, 33, 34, 37, 38, ... %t A376602 Join@@Position[Differences[Select[Range[100],CompositeQ],2],0] %Y A376602 Partitions into composite numbers are counted by A023895, factorizations A050370. %Y A376602 For prime instead of composite we have A064113. %Y A376602 These are the positions of zeros in A073445. %Y A376602 For first differences we had A073783, ones A375929, complement A065890. %Y A376602 For concavity in primes we have A258025/A258026, weak A333230/A333231. %Y A376602 For upward concavity (instead of zero) we have A376651, downward A376652. %Y A376602 The complement is A376603. %Y A376602 For composite numbers: A002808 (terms), A073783 (first differences), A073445 (second differences), A376603 (nonzero curvature), A376651 (concave-up), A376652 (concave-down). %Y A376602 For inflection and undulation points: A064113 (prime), A376588 (non-perfect-power), A376591 (squarefree), A376594 (nonsquarefree), A376597 (prime-power), A376600 (non-prime-power). %Y A376602 Cf. A000040, A036263, A251092, A333214, A333216, A333254. %K A376602 nonn %O A376602 1,2 %A A376602 _Gus Wiseman_, Oct 05 2024