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A238894
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).
2
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, 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, 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0
OFFSET
1,53
COMMENTS
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.
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.
EXAMPLE
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.
MATHEMATICA
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]
CROSSREFS
Cf. A083309.
Sequence in context: A253607 A212179 A257023 * A054740 A272947 A177740
KEYWORD
nonn,tabf
AUTHOR
T. D. Noe, Mar 07 2014
STATUS
approved