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 A133832 #9 Sep 30 2024 09:15:15
%S A133832 2,3,5,13,6,7,9,9,18,19,14,13,15,17,17,81,20,19,30,33,26,27,38,81,27,
%T A133832 35,31,33,35,31,42,458465,36,45,47,37,67,53,41,57,42,45,46,69,54,57,
%U A133832 53,1009,100,119,55,73,83,67,57,1265,74,69,66,113,75,101,66,2241,68,67,70
%N A133832 Least number k > n such that the binary trinomial 1 + 2^n + 2^k is prime, or 0 if there is no such k.
%C A133832 Conjecture: a(n) is nonzero for all n. These binary trinomials can also be written as f*2^n+1, where f=2^m+1 for some m, which is reminiscent of the Sierpinski problem (see A076336). The conjecture is equivalent to no Sierpinski numbers of the form 2^m+1 existing.
%C A133832 The PFGW program was used to find a(32), which produces a 138012-digit probable prime.
%H A133832 T. D. Noe, <a href="/A133832/b133832.txt">Table of n, a(n) for n=1..255</a>
%H A133832 Henri Lifchitz and Renaud Lifchitz (Editors), <a href="http://www.primenumbers.net/prptop/searchform.php?form=2%5En%2B2%5Em%2B1">Search for 2^n+2^m+1</a>, PRP Top Records.
%t A133832 mx=4000; Table[s=1+2^n; k=n+1; While[k<mx && !PrimeQ[s+2^k], k++ ]; If[k==mx, 0, k], {n,100}]
%Y A133832 Cf. A057732, A059242, A057196, A057200, A081091 (various forms of prime binary trinomials).
%Y A133832 Cf. A095056, A133830 (k < n equivalent), A133831.
%K A133832 nonn
%O A133832 1,1
%A A133832 _T. D. Noe_, Sep 26 2007
%E A133832 Edited by _Peter Munn_, Sep 29 2024