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 A129508 #18 Aug 01 2025 17:05:05
%S A129508 0,1,10,12,27,30,31,36,37,252,255,256,280,282,756,757,760,810,811,
%T A129508 3160,3162,3186,3187,3250,3252,3276,3277,3280,6561,6562,6885,6886,
%U A129508 6912,6925,7536,7537,7560,7561,7626,7627,7650,7651,19686,19687,20007,20010,20011
%N A129508 Numbers k such that 3 and 5 do not divide binomial(2*k, k).
%C A129508 The Erdos paper proves that for any two odd primes p and q, there are an infinite number of k for which gcd(p*q, binomial(2*k, k)) = 1; i.e., p and q do not divide binomial(2*k, k).
%H A129508 T. D. Noe, <a href="/A129508/b129508.txt">Table of n, a(n) for n = 1..1000</a>
%H A129508 P. Erdos, R. L. Graham, I. Z. Russa, and E. G. Straus, <a href="https://users.renyi.hu/~p_erdos/1975-27.pdf">On the prime factors of C(2n,n)</a>, Math. Comp. 29 (1975), 83-92.
%F A129508 Intersection of A005836 and A037453.
%t A129508 lim=10000; Intersection[Table[FromDigits[IntegerDigits[k,2],3], {k,0,lim}], Table[FromDigits[IntegerDigits[k,3],5], {k,0,lim}]]
%o A129508 (PARI) valp(n, p)=my(s); while(n\=p, s+=n); s
%o A129508 is(n)=valp(2*n, 3)==2*valp(n, 3) && valp(2*n, 5)==2*valp(n, 5) \\ _Charles R Greathouse IV_, Feb 03 2016
%Y A129508 Cf. A030979 (k such that 3, 5 and 7 do not divide binomial(2*k, k)).
%K A129508 nonn
%O A129508 1,3
%A A129508 _T. D. Noe_, Apr 18 2007