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A010330
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n such C(n,3) = C(x,3) + C(y,3) is solvable.
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2
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6, 17, 57, 60, 76, 111, 112, 121, 142, 177, 247, 296, 420, 437, 454, 476, 494, 530, 537, 552, 564, 590, 646, 690, 704, 716, 742, 749, 755, 820, 870, 910, 920, 1100, 1160, 1222, 1243, 1430, 1436, 1446, 1452, 1647, 1710, 1740, 1788, 1870, 2172, 2185, 2222, 2258
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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"!).
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REFERENCES
| J. Leech, Some solutions of Diophantine equations, Proc. Camb. Phil. Soc., 53 (1957), 778-780.
Van der Poorten, Notes on Fermat's Last Theorem, Wiley, p. 122.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..463 (n < 10^6)
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EXAMPLE
| C(10,3)+C(16,3)=C(17,3)=680.
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MATHEMATICA
| 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)&] (* From Jean-François Alcover, Mar 30 2011 *)
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CROSSREFS
| Cf. A034404.
Sequence in context: A083334 A199113 A088016 * A109311 A151350 A195741
Adjacent sequences: A010327 A010328 A010329 * A010331 A010332 A010333
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from David W. Wilson (davidwwilson(AT)comcast.net)
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