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%I #11 Mar 09 2014 16:35:13
%S 1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,1,0,
%T 0,1,1,0,0,1,0,1,0,1,1,0,1,1,1,1,1,1,2,1,2,1,2,2,1,2,2,2,1,2,2,2,1,2,
%U 2,2,1,2,2,1,2,1,2,1,1,1,1,1,1,0,1,1,0
%N Irregular triangle of the number of times that sums +- 3 +- 5 +- 7 +- 11 +-...+- prime(2n+1) equal an even number in the range -d to d, where d = 3 + 5 + 7 + 11 +...+ prime(2n+1).
%C Because the value at odd numbers is zero, we count only the values at even numbers. This sequence, a generalization of A083309, is more interesting plotted.
%C The rows of the irregular triangle begin at positions 1, 10, 37, 94, 193, 352, 589, 916, 1355, 1922, 2633, 3506, 4565, 5828, and 7307. having lengths 9, 27, 57, 99, 159, 237, 327, 439, 567, 711, 873, 1059, 1263, 1479, and 1719.
%H T. D. Noe, <a href="/A238894/b238894.txt">Rows n = 1..15 of irregular triangle, flattened</a>
%H T. D. Noe, <a href="http://www.sspectra.com/math/Sums.html">Extremal Sums of Sequences</a>
%e The first row of the irregular triangle is {1, 0, 0, 1, 0, 1, 0, 0, 1} because the sums +- 3 +- 5 form the numbers -8, -2, 2, and 8. The odd numbers are suppressed.
%t nMax = 10; d = {1, 0, 0, 1}; t = {}; Do[p = Prime[n + 1]; d = PadLeft[d, Length[d] + p] + PadRight[d, Length[d] + p]; If[0 == Mod[n, 2], AppendTo[t, d]], {n, 2, nMax}]; Flatten[t]
%Y Cf. A083309.
%K nonn,tabf
%O 1,53
%A _T. D. Noe_, Mar 07 2014