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 A373672 #12 Jun 20 2024 16:58:22 %S A373672 5,3,1,6,1,1,2,1,3,1,3,1,2,1,1,1,3,2,2,1,3,1,1,1,4,1,1,1,2,1,1,1,1,1, %T A373672 2,1,3,1,3,1,2,1,1,1,1,1,2,1,3,2,1,1,1,3,1,1,1,1,1,1,1,3,1,1,1,2,1,1, %U A373672 1,2,1,3,1,2,1,1,1,3,1,1,1,1,1,1,1,3,1 %N A373672 Length of the n-th maximal antirun of non-prime-powers. %C A373672 An antirun of a sequence (in this case A361102 or A024619 with 1) is an interval of positions at which consecutive terms differ by more than one. %H A373672 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>. %F A373672 Partial sums are A356068(A255346(n)). %e A373672 The maximal antiruns of non-prime-powers begin: %e A373672 1 6 10 12 14 %e A373672 15 18 20 %e A373672 21 %e A373672 22 24 26 28 30 33 %e A373672 34 %e A373672 35 %e A373672 36 38 %e A373672 39 %e A373672 40 42 44 %e A373672 45 %e A373672 46 48 50 %t A373672 Length/@Split[Select[Range[100],!PrimePowerQ[#]&],#1+1!=#2&]//Most %Y A373672 For prime antiruns we have A027833. %Y A373672 For nonsquarefree runs we have A053797, firsts A373199. %Y A373672 For non-prime-powers runs we have A110969, firsts A373669, sorted A373670. %Y A373672 For squarefree runs we have A120992. %Y A373672 For prime-power runs we have A174965. %Y A373672 For prime runs we have A175632. %Y A373672 For composite runs we have A176246, firsts A073051, sorted A373400. %Y A373672 For squarefree antiruns we have A373127, firsts A373128. %Y A373672 For composite antiruns we have A373403. %Y A373672 For antiruns of prime-powers: %Y A373672 - length A373671 %Y A373672 - min A120430 %Y A373672 - max A006549 %Y A373672 For antiruns of non-prime-powers: %Y A373672 - length A373672 (this sequence), firsts (3,7,2,25,1,4) %Y A373672 - min A373575 %Y A373672 - max A255346 %Y A373672 A000961 lists all powers of primes. A246655 lists just prime-powers. %Y A373672 A057820 gives first differences of consecutive prime-powers, gaps A093555. %Y A373672 A356068 counts non-prime-powers up to n. %Y A373672 A361102 lists all non-prime-powers (A024619 if not including 1). %Y A373672 Cf. A001359, A008864, A014963, A038664, A054265, A067774, A251092, A373401. %K A373672 nonn %O A373672 1,1 %A A373672 _Gus Wiseman_, Jun 14 2024