A062527 Smallest number (>1) which appears at least n times in Pascal's triangle.

2, 3, 6, 10, 120, 120, 3003, 3003

Offset

1,1

Comments

Singmaster's conjecture is that this sequence is finite.

Links

Table of n, a(n) for n=1..8.

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