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A373406 Sum of the n-th maximal run of odd primes differing by two.

%I A373406 #11 Jun 07 2024 09:21:54
%S A373406 15,24,36,23,60,37,84,47,53,120,67,144,79,83,89,97,204,216,113,127,
%T A373406 131,276,300,157,163,167,173,360,384,396,211,223,456,233,480,251,257,
%U A373406 263,540,277,564,293,307,624,317,331,337,696,353,359,367,373,379,383
%N A373406 Sum of the n-th maximal run of odd primes differing by two.
%C A373406 The length of this run is given by A251092.
%C A373406 For this sequence we define a run to be an interval of positions at which consecutive terms differ by two. Normally, a run has consecutive terms differing by one, but odd prime numbers already differ by at least two.
%C A373406 Contains A054735 (sums of twin prime pairs) without its first two terms and A007510 (non-twin primes) as subsequences. - _R. J. Mathar_, Jun 07 2024
%H A373406 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>
%e A373406 Row-sums of:
%e A373406    3   5   7
%e A373406   11  13
%e A373406   17  19
%e A373406   23
%e A373406   29  31
%e A373406   37
%e A373406   41  43
%e A373406   47
%e A373406   53
%e A373406   59  61
%e A373406   67
%e A373406   71  73
%e A373406   79
%e A373406   83
%e A373406   89
%e A373406   97
%t A373406 Total/@Split[Select[Range[3,100],PrimeQ],#1+2==#2&]//Most
%Y A373406 The partial sums are a subset of A071148 (partial sums of odd primes).
%Y A373406 Functional neighbors: A025584, A054265, A067774, A251092 (or A175632), A373405, A373413, A373414.
%Y A373406 A000040 lists the primes, differences A001223.
%Y A373406 A046933 counts composite numbers between primes.
%Y A373406 A065855 counts composite numbers up to n.
%Y A373406 Cf. A005117, A007053, A029707, A038664, A293697, A350842, A371201.
%K A373406 nonn
%O A373406 1,1
%A A373406 _Gus Wiseman_, Jun 05 2024