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 A376680 #6 Oct 10 2024 08:52:44 %S A376680 2,2,2,2,2,2,1,4,2,4,1,2,2,2,1,4,1,4,2,4,1,2,2,4,1,2,1,4,1,6,1,2,2,2, %T A376680 2,2,1,12,1,2,1,4,2,8,2,4,1,4,1,2,1,4,1,4,2,8,2,2,2,10,1,10,1,2,2,2,1, %U A376680 4,2,8,1,4,1,4,1,4,2,4,1,2,2,8,1,12,1,2 %N A376680 Run-lengths of first differences of composite numbers. %C A376680 Also first differences of A376603 (points of nonzero curvature in the composite numbers). %e A376680 The composite numbers (A002808) are: %e A376680 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, ... %e A376680 with first differences (A073783): %e A376680 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, ... %e A376680 with runs: %e A376680 (2,2), (1,1), (2,2), (1,1), (2,2), (1,1), (2), (1,1,1,1), (2,2), (1,1,1,1), ... %e A376680 with lengths (A376680): %e A376680 2, 2, 2, 2, 2, 2, 1, 4, 2, 4, 1, 2, 2, 2, 1, 4, 1, 4, 2, 4, 1, 2, 2, 4, 1, 2, ... %t A376680 Length/@Split[Differences[Select[Range[100],CompositeQ]]] %Y A376680 These are the run-lengths of A073783, ones A375929. %Y A376680 For prime instead of composite we have A333254, first appearances A335406. %Y A376680 These are the first differences of A376603. %Y A376680 A000040 lists the prime numbers, first differences A001223, second differences A036263. %Y A376680 A002808 lists the composite numbers, differences A073783. %Y A376680 A064113 lists positions of adjacent equal prime gaps. %Y A376680 A073445 gives second differences of composite numbers, zeros A376602. %Y A376680 Cf. A054546, A076259, A174965, A251092, A376651, A376652. %K A376680 nonn %O A376680 1,1 %A A376680 _Gus Wiseman_, Oct 10 2024