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 A129515 #18 Sep 03 2025 00:49:25
%S A129515 87,199,237,467,607,967,1127,1319,1483,1903,1943,2012,2047,2287,2348,
%T A129515 2359,2464,2479,2495,2507,2623,2645,2719,3349,3467,3514,3568,3629,
%U A129515 3633,3712,3847,3919,4088,4224,4287,4360,4479,4927,4987,5087,5167,5224,5669
%N A129515 Numbers m such that binomial(2*m, m) has the same prime factors as binomial(2*k, k) for some k > m.
%C A129515 The Erdős paper mentions 87 and 607. The paper conjectures that the sequence is infinite. For the m listed here, k=m+1. Note that we need only examine k such that pi(2*m) = pi(2*k), where pi is the prime counting function.
%H A129515 Charles R Greathouse IV, <a href="/A129515/b129515.txt">Table of n, a(n) for n = 1..10000</a> (corrected and extended from original by T. D. Noe)
%H A129515 Thomas Bloom, <a href="https://www.erdosproblems.com/730">Problem 730</a>, Erdős Problems.
%H A129515 P. Erdős, R. L. Graham, I. Z. Russa and E. G. Straus, <a href="http://dx.doi.org/10.1090/S0025-5718-1975-0369288-3">On the prime factors of C(2n,n)</a>, Math. Comp. 29 (1975), 83-92.
%t A129515 s={}; nLst={}; t={}; Do[p=Transpose[FactorInteger[Binomial[2n,n]]][[1]]; If[s!={} && p[[ -1]]!=s[[ -1,-1]], s={}; nLst={}]; pos=Position[s,p,1,1]; If[pos!={}, m=pos[[1,1]]; AppendTo[t,nLst[[m]]], AppendTo[s,p]; AppendTo[nLst,n]], {n,10000}]; t
%o A129515 (PARI) valp(n,p)=my(s); while(n\=p, s+=n); s
%o A129515 f(n,p)=valp(2*n,p)==2*valp(n,p)
%o A129515 is(n)=for(k=n+1,nextprime(2*n)\2, forprime(p=2,2*n, if(f(n,p)!=f(k,p), next(2))); return(k)); 0 \\ _Charles R Greathouse IV_, Oct 18 2017
%Y A129515 Cf. A067434 (number of distinct prime factors in binomial(2n, n)).
%K A129515 nonn,changed
%O A129515 1,1
%A A129515 _T. D. Noe_, Apr 18 2007