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%I #23 Jun 13 2021 03:22:40
%S 6,17,57,60,76,111,112,121,142,177,247,296,420,437,454,476,494,530,
%T 537,552,564,590,646,690,704,716,742,749,755,820,870,910,920,1100,
%U 1160,1222,1243,1430,1436,1446,1452,1647,1710,1740,1788,1870,2172,2185,2222,2258
%N Numbers k such that C(k,3) = C(x,3) + C(y,3) is solvable.
%C Bombieri's Napkin Problem: Bombieri said that "the equation C(x,n)+C(y,n)=C(z,n) has no trivial solutions for n >= 3" (the joke being that he said "trivial" rather than "nontrivial"!).
%D J. Leech, Some solutions of Diophantine equations, Proc. Camb. Phil. Soc., 53 (1957), 778-780.
%D Van der Poorten, Notes on Fermat's Last Theorem, Wiley, p. 122.
%H T. D. Noe, <a href="/A010330/b010330.txt">Table of n, a(n) for n = 1..463</a> (n < 10^6)
%F a(n) = A002311(n) + 2. - _Reinhard Zumkeller_, May 02 2014
%e C(10,3) + C(16,3) = C(17,3) = 680, so 17 is a term.
%t f[n_]:=Reduce[1 < x <= y < n && n(n-1)(n-2) == x(x-1)(x-2) + y(y-1)(y-2), {x,y}, Integers]; Select[Range[2260], (f[#] =!= False)&] (* _Jean-François Alcover_, Mar 30 2011 *)
%o (Haskell)
%o a010330 = (+ 2) . a002311 -- _Reinhard Zumkeller_, May 02 2014
%Y Cf. A034404.
%Y Cf. A000292.
%K nonn,nice
%O 1,1
%A _N. J. A. Sloane_
%E More terms from _David W. Wilson_
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