A099473 Numbers k such that binomial(2*k,k) cannot be represented as the sum of three squares.

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A099470 A099471 A099472 * A099474 A099475 A099476

Keyword

nonn

Author

T. D. Noe, Oct 18 2004

Status

approved