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 A373823 #6 Jun 22 2024 22:09:07 %S A373823 2,2,1,2,1,2,3,1,3,2,1,2,6,1,3,2,1,3,2,3,4,2,1,2,1,2,7,2,3,1,5,1,6,2, %T A373823 6,1,5,1,2,1,12,2,1,2,3,1,5,9,1,3,2,1,5,7,2,1,2,7,3,5,1,2,3,4,6,2,3,4, %U A373823 2,4,5,1,5,1,3,2,3,4,2,1,2,6,4,2,4,2,3 %N A373823 Half the sum of the n-th maximal run of first differences of odd primes. %C A373823 Halved run-sums of A001223. %e A373823 The odd primes are: %e A373823 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, ... %e A373823 with first differences: %e A373823 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, ... %e A373823 with runs: %e A373823 (2,2), (4), (2), (4), (2), (4), (6), (2), (6), (4), (2), (4), (6,6), ... %e A373823 with halved sums a(n). %t A373823 Total/@Split[Differences[Select[Range[3,1000],PrimeQ]]]/2 %Y A373823 Halved run-sums of A001223. %Y A373823 For run-lengths we have A333254, run-lengths of run-lengths A373821. %Y A373823 Multiplying by two gives A373822. %Y A373823 A000040 lists the primes. %Y A373823 A027833 gives antirun lengths of odd primes (partial sums A029707). %Y A373823 A046933 counts composite numbers between primes. %Y A373823 A065855 counts composite numbers up to n. %Y A373823 A071148 gives partial sums of odd primes. %Y A373823 A373820 gives run-lengths of antirun-lengths of odd primes. %Y A373823 For prime runs: A001359, A006512, A025584, A067774, A373405, A373406. %Y A373823 Cf. A037201, A038664, A054265, A176246, A251092, A373404, A373825. %K A373823 nonn %O A373823 1,1 %A A373823 _Gus Wiseman_, Jun 22 2024