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 A258126 #19 Jul 01 2015 20:15:27
%S A258126 2,3,7,5,31,7,29,37,0,11,67,13,1093,1471,9949,17,131071,19,191,211,
%T A258126 7547,23,277,190051,1807781,61450327,379,29,0,31,36457,1149017,0,0,
%U A258126 631,37,0,0,0,41,0,43,947,991,0,47,1129,8682997471,0,1125899906842573,1327,53
%N A258126 Smallest prime of the form Sum_{i=0..k} binomial(n,i), or a(n)=0 if there is no such a prime.
%C A258126 a(n)=0 for n=9,29,33,34,37,38,39,41,45,49,...;
%C A258126 records a(n) are on the positions: 1,2,3,5,8,11,13,14,15,17,24,25,26,48,50,...
%C A258126 Mersenne primes a(n) = 2^n-1 are at positions 2,3,5,17,...
%H A258126 Peter J. C. Moses, <a href="/A258126/b258126.txt">Table of n, a(n) for n = 1..1000</a>
%F A258126 a(n) <= 2^n-1.
%o A258126 (PARI) a(n) = {my(k = 0); while(! isprime(p=sum(i=0, k, binomial(n,i))), k++; if ((k>n) && !isprime(binomial(n,k)), return (0);)); p;} \\ _Michel Marcus_, May 23 2015
%Y A258126 Cf. A007318, A258127.
%K A258126 nonn
%O A258126 1,1
%A A258126 _Vladimir Shevelev_, May 21 2015
%E A258126 More terms from _Peter J. C. Moses_, May 21 2015