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 A376651 #12 Oct 19 2024 08:34:41 %S A376651 4,8,12,17,23,26,30,35,40,46,49,55,58,63,70,73,77,81,94,97,102,112, %T A376651 118,123,126,131,136,146,150,162,173,176,180,185,195,200,205,210,216, %U A376651 219,229,242,245,249,262,267,276,280,285,292,297,302,305,310,317,320 %N A376651 Points of upward concavity in the sequence of composite numbers (A002808). %C A376651 These are points at which the second differences (A073445) are positive. %C A376651 Also positions of strict ascents in the first differences (A073783) of composite numbers (A002808). %H A376651 Dominic McCarty, <a href="/A376651/b376651.txt">Table of n, a(n) for n = 1..1000</a> %H A376651 Gus Wiseman, <a href="/A376651/a376651.png">Points of upward concavity in the sequence of composite numbers</a>. %e A376651 The composite numbers are (A002808): %e A376651 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, ... %e A376651 with first differences (A073783): %e A376651 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 A376651 with first differences (A073445): %e A376651 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 A376651 with positive terms at (A376651): %e A376651 4, 8, 12, 17, 23, 26, 30, 35, 40, 46, 49, 55, 58, 63, 70, 73, 77, 81, 94, 97, ... %t A376651 Join@@Position[Sign[Differences[Select[Range[1000],CompositeQ],2]],1] %Y A376651 The version for A000002 is A022297, negative A156242. %Y A376651 Partitions into composite numbers are counted by A023895, factorizations A050370. %Y A376651 For first differences we had A065310 or A073783, ones A375929. %Y A376651 These are the positions of positive terms in A073445, negative A376652. %Y A376651 For prime instead of composite we have A258025, negative A258026. %Y A376651 For zero second differences (instead of positive) we have A376602. %Y A376651 For composite numbers: A002808 (terms), A073783 (first differences), A073445 (second differences), A376602 (inflections and undulations), A376603 (nonzero curvature), A376652 (concave-down). %Y A376651 Cf. A000961, A057820, A064113, A065890, A251092, A333254, A376604. %K A376651 nonn %O A376651 1,1 %A A376651 _Gus Wiseman_, Oct 06 2024