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 A133831 #15 Sep 30 2024 09:15:04
%S A133831 2,1,1,1,2,1,1,9,3,3,2,1,4,5,1,1,11,1,6,5,4,7,3,9,27,17,15,1,15,1,6,
%T A133831 458465,4,9,14,13,3,11,25,57,6,7,46,17,7,15,2,1009,30,23,6,21,2,33,1,
%U A133831 1265,3,69,14,5,6,21,19,2241,30,3,1,5,34,19,26,17,19,17,5,33,15,23,27
%N A133831 Least positive number k != n such that the binary trinomial 1 + 2^n + 2^k is prime, or 0 if there is no such k.
%C A133831 Does such k exist (so that 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). Hence if there are no Sierpinski numbers of the form 2^m+1, then a(n) is nonzero for all n.
%C A133831 The PFGW program was used to find a(32), which produces a 138012-digit probable prime. If a(256) is nonzero, it is greater than 10^6.
%H A133831 T. D. Noe, <a href="/A133831/b133831.txt">Table of n, a(n) for n = 1..255</a>
%H A133831 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 A133831 mx=4000; Table[s=1+2^n; k=1; While[k==n || (k<mx && !PrimeQ[s+2^k]), k++ ]; If[k==mx, 0, k], {n,100}]
%Y A133831 Cf. A057732, A059242, A057196, A057200, A081091 (various forms of prime binary trinomials).
%Y A133831 Closely related problems: A040076 (see also A076336), A067760, A133830 (k < n), A133832 (k > n).
%Y A133831 Cf. A095056.
%K A133831 nonn
%O A133831 1,1
%A A133831 _T. D. Noe_, Sep 26 2007
%E A133831 Edited by _Peter Munn_, Sep 29 2024