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 A258127 #11 Jul 01 2015 20:16:57
%S A258127 1,1,2,1,4,1,2,2,0,1,2,1,4,4,6,1,16,1,2,2,4,1,2,6,8,16,2,1,0,1,4,6,0,
%T A258127 0,2,1,0,0,0,1,0,1,2,2,0,1,2,10,0,48,2,1,36,20,6,2,8,1,10,1,16,13,2,2,
%U A258127 0,1,0,2,0,1,2,1,0,0,2,2,0,1,8,74,64,1,16
%N A258127 Smallest k such that Sum_{i=0..k} binomial(n,i) is prime, or a(n)=0 if there is no such k.
%C A258127 a(n)=0 for n=9,29,33,34,37,38,39,41,45,49,...;
%C A258127 records a(n) are 1,2,4,6,16,48,74,...
%C A258127 at positions 1,3,5,15,17,50,80,...
%H A258127 Peter J. C. Moses, <a href="/A258127/b258127.txt">Table of n, a(n) for n = 1..1000</a>
%F A258127 a(n) <= n-1.
%o A258127 (PARI) a(n) = {my(k = 0); while(! isprime(sum(i=0, k, binomial(n,i))), k++; if ((k>n) && !isprime(binomial(n,k)), return (0);)); k;} \\ _Michel Marcus_, May 23 2015
%Y A258127 Cf. A007318, A258126.
%K A258127 nonn
%O A258127 1,3
%A A258127 _Vladimir Shevelev_, May 21 2015
%E A258127 More terms from _Peter J. C. Moses_, May 21 2015