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 A159260 #6 Sep 12 2019 19:44:42
%S A159260 1,2,4,5,8,43,127,251,1903
%N A159260 Numbers k such that 1 + Sum_{i=1..k} 2^prime(i) is prime.
%C A159260 See A159261 for the primes produced by these n. See A159262 for prime(n), the largest exponent in the sum. The term 1903 produces a probable prime; smaller n produce provable primes. See A122035 for the reducibility of the polynomial obtained by replacing 2 by x.
%e A159260 1 is here because 1 + 2^2 = 5 is prime.
%e A159260 2 is here because 1 + 2^2 + 2^3 = 13 is prime.
%e A159260 4 is here because 1 + 2^2 + 2^3 + 2^5 + 2^7 = 173 is prime.
%e A159260 5 is here because 1 + 2^2 + 2^3 + 2^5 + 2^7 + 2^11 = 2111 is prime.
%t A159260 s=1; Reap[Do[s=s+2^Prime[n]; If[PrimeQ[s], Sow[n]], {n,2000}]][[2,1]]
%K A159260 nonn
%O A159260 1,2
%A A159260 _T. D. Noe_, Apr 07 2009