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