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

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

Offset: 1

Author

Henry Bottomley, Jul 10 2001

Keywords

• nonn
• nice

Comments

Singmaster's conjecture is that this sequence is finite.

Examples

			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).
		

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.

Crossrefs

Cf. A003015, A003016, A006987, A007318, A059233.

Programs

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 *)