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 A373822 #7 Jun 22 2024 22:09:11 %S A373822 4,4,2,4,2,4,6,2,6,4,2,4,12,2,6,4,2,6,4,6,8,4,2,4,2,4,14,4,6,2,10,2, %T A373822 12,4,12,2,10,2,4,2,24,4,2,4,6,2,10,18,2,6,4,2,10,14,4,2,4,14,6,10,2, %U A373822 4,6,8,12,4,6,8,4,8,10,2,10,2,6,4,6,8,4,2,4 %N A373822 Sum of the n-th maximal run of first differences of odd primes. %C A373822 Run-sums of A001223. For run-lengths instead of run-sums we have A333254. %e A373822 The odd primes are %e A373822 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, ... %e A373822 with first differences %e A373822 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, ... %e A373822 with runs %e A373822 (2,2), (4), (2), (4), (2), (4), (6), (2), (6), (4), (2), (4), (6,6), ... %e A373822 with sums a(n). %t A373822 Total/@Split[Differences[Select[Range[3,1000],PrimeQ]]] %Y A373822 Run-sums of A001223. %Y A373822 For run-lengths we have A333254, run-lengths of run-lengths A373821. %Y A373822 Dividing by two gives A373823. %Y A373822 A000040 lists the primes. %Y A373822 A027833 gives antirun lengths of odd primes (partial sums A029707). %Y A373822 A046933 counts composite numbers between primes. %Y A373822 A065855 counts composite numbers up to n. %Y A373822 A071148 gives partial sums of odd primes. %Y A373822 A373820 gives run-lengths of antirun-lengths of odd primes. %Y A373822 For prime runs: A001359, A006512, A025584, A067774, A373405, A373406. %Y A373822 Cf. A037201, A038664, A054265, A176246, A251092, A373404, A373825. %K A373822 nonn %O A373822 1,1 %A A373822 _Gus Wiseman_, Jun 22 2024