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 A062527 Smallest number (>1) which appears at least n times in Pascal's triangle. 2
 2, 3, 6, 10, 120, 120, 3003, 3003 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Singmaster's conjecture is that this sequence is finite. LINKS H. L. Abbott, P. Erdos and D. Hanson, On the numbers of times an integer occurs as a binomial coefficient, Amer. Math. Monthly, (1974), 256-261. FTL Magazine, One Thousand and One Coincidences D. Singmaster, How often does an integer occur as a binomial coefficient?, Amer. Math. Monthly, 78 (1971), 385-386. David Singmaster, Repeated binomial coefficients and Fibonacci numbers, Fibonacci Quarterly 13 (1975) 295-298. EXAMPLE a(8)=3003 since 3003 =C(3003,1) =C(3003,3002) =C(78,2) =C(78,76) =C(15,5) =C(15,10) =C(14,6) = C(14,8). MATHEMATICA (* Computation lasts a few minutes *) max = 4000; Clear[cnt]; cnt[_] = 0; Do[b = Binomial[n, k]; If[b <= max, cnt[b] += 1], {n, 0, max}, {k, 1, n - 1}]; sel = Select[Table[{b, cnt[b]}, {b, 1, max }], #[[2]] >= 1&]; a[n_] := Select[sel, #[[2]] >= n&][[1, 1]]; Array[a, 8] (* Jean-François Alcover, Oct 05 2015 *) CROSSREFS Cf. A003015, A003016, A006987, A007318, A059233. Sequence in context: A054357 A056606 A186408 * A296444 A038752 A125714 Adjacent sequences:  A062524 A062525 A062526 * A062528 A062529 A062530 KEYWORD nonn,nice AUTHOR Henry Bottomley, Jul 10 2001 STATUS approved

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Last modified June 26 00:10 EDT 2019. Contains 324367 sequences. (Running on oeis4.)