This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A062527 #14 Jan 05 2025 19:51:36
%S A062527 2,3,6,10,120,120,3003,3003
%N A062527 Smallest number (>1) which appears at least n times in Pascal's triangle.
%C A062527 Singmaster's conjecture is that this sequence is finite.
%H A062527 H. L. Abbott, P. Erdos and D. Hanson, <a href="http://www.jstor.org/stable/2319526">On the numbers of times an integer occurs as a binomial coefficient</a>, Amer. Math. Monthly, (1974), 256-261.
%H A062527 FTL Magazine, <a href="http://www.cthisspace.com/ftl/macaw/MR46.html">One Thousand and One Coincidences</a>
%H A062527 D. Singmaster, <a href="http://www.jstor.org/stable/2316907">How often does an integer occur as a binomial coefficient?</a>, Amer. Math. Monthly, 78 (1971), 385-386.
%H A062527 David Singmaster, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/13-4/singmaster.pdf">Repeated binomial coefficients and Fibonacci numbers</a>, Fibonacci Quarterly 13 (1975) 295-298.
%e A062527 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).
%t A062527 (* 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 *)
%Y A062527 Cf. A003015, A003016, A006987, A007318, A059233.
%K A062527 nonn,nice
%O A062527 1,1
%A A062527 _Henry Bottomley_, Jul 10 2001