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%I #7 Oct 01 2017 10:01:48
%S 1,2,3,4,5,9,14,17,18,20,21,35,41
%N Numbers n such that binomial(n,m) cannot be represented as the sum of three squares for any 0 <= m <= n.
%H Andrew Granville and Yiliang Zhu, <a href="http://www.dms.umontreal.ca/~andrew/PDF/YZhu.pdf">Representing binomial coefficients as sums of squares</a>, Amer. Math. Monthly, Vol. 97, No. 6 (1990), 486-493.
%t 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]]&]
%Y Cf. A004215 (sums of 4 but no fewer nonzero squares), A099473.
%K fini,full,nonn
%O 1,2
%A _T. D. Noe_, Oct 18 2004