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A099473
Numbers k such that binomial(2*k,k) cannot be represented as the sum of three squares.
2
5, 6, 12, 24, 27, 30, 39, 48, 57, 60, 71, 85, 86, 90, 96, 106, 111, 113, 119, 120, 123, 126, 135, 159, 172, 180, 192, 212, 225, 240, 249, 252, 263, 287, 293, 294, 297, 306, 329, 344, 347, 350, 360, 363, 365, 378, 384, 402, 424, 427, 429, 437, 438, 447, 449, 479
OFFSET
1,1
COMMENTS
Granville and Zhu show that the density of these numbers is 1/8.
LINKS
Andrew Granville and Yiliang Zhu, Representing binomial coefficients as sums of squares, Amer. Math. Monthly, Vol. 97, No. 6 (1990), pp. 486-493; alternative link.
MATHEMATICA
NoRepAs3Sqrs[n_] := Module[{e2}, e2=IntegerExponent[n, 2]; If[EvenQ[e2], 7==Mod[n/2^e2, 8], False]]; Select[Range[500], NoRepAs3Sqrs[Binomial[2#, # ]]&]
CROSSREFS
Cf. A004215 (sums of 4 but no fewer nonzero squares), A099472.
Sequence in context: A126593 A302300 A173074 * A051572 A344221 A348155
KEYWORD
nonn
AUTHOR
T. D. Noe, Oct 18 2004
STATUS
approved