A099472 Numbers n such that binomial(n,m) cannot be represented as the sum of three squares for any 0 <= m <= n.

1, 2, 3, 4, 5, 9, 14, 17, 18, 20, 21, 35, 41

Offset

1,2

Links

Table of n, a(n) for n=1..13.

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[200], {}==Flatten[Position[Table[NoRepAs3Sqrs[Binomial[ #, m]], {m, #}], True]]&]

Crossrefs

Cf. A004215 (sums of 4 but no fewer nonzero squares), A099473.

Sequence in context: A217376 A050160 A230769 * A191321 A222432 A222433

Adjacent sequences: A099469 A099470 A099471 * A099473 A099474 A099475

Keyword

fini,full,nonn

Author

T. D. Noe, Oct 18 2004

Status

approved