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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.
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
Sequence in context: A056606 A371505 A186408 * A296444 A038752 A125714
KEYWORD
nonn,nice
AUTHOR
Henry Bottomley, Jul 10 2001
STATUS
approved

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Last modified May 18 07:16 EDT 2024. Contains 372618 sequences. (Running on oeis4.)