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A099473 Numbers n such that binomial(2n,n) cannot be represented as the sum of three squares. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Granville and Zhu show that the density of these numbers is 1/8.

LINKS

Table of n, a(n) for n=1..56.

Andrew Granville and Yiliang Zhu, Representing binomial coefficients as sums of squares, Amer. Math. Monthly, Vol. 97, No. 6 (1990), 486-493.

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 A047436 A061437

Adjacent sequences:  A099470 A099471 A099472 * A099474 A099475 A099476

KEYWORD

nonn

AUTHOR

T. D. Noe, Oct 18 2004

STATUS

approved

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Last modified October 14 05:08 EDT 2019. Contains 327995 sequences. (Running on oeis4.)