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 A144315 #3 Mar 31 2012 10:28:53
%S A144315 149,233,317,569,653,1493,1913,1997,2417,2837,3089,3593,3677,3761,
%T A144315 3929,4013,4349,4517,4937,5021,5189,5273,5441,5693,6197,6449,6869,
%U A144315 7457,7541,7793,8297,8969,9137,9221,9473,10061,10313,10733,11069,11321,11489
%N A144315 Prime numbers p such that p - 1 is the fourth a-figurate number, eighth b-figurate number and possibly sixteenth c-figurate number for some a, b and c and not a d-figurate number for any nontrivial d.
%C A144315 The 37th Mersenne prime exponent (Mpe, A000043) 3021377 is a member: 3021376 is the fourth 503564-figurate number, the eighth 107908-figurate number and the sixteenth 25180-figurate number and is not a k-figurate number for any other k except 3021376 (trivially). The 44th Mersenne prime exponent 32582657 is not a member of this sequence; however, it is a (4, 8, 16, 64) k-figurate number.
%C A144315 It is conjectured:
%C A144315 - that this sequence is infinite;
%C A144315 - that there is a unique set {4, 8, 16, 64, ...} (A074700?) giving the possible orders in k-figurate numbers for the set S of all Mpe for which Mpe - 1 is a (4, 8) k-figurate number;
%C A144315 - that the ratio of Mpe in this sequence to those not approaches a nonzero value;
%C A144315 - that a characteristic function f(n) exists which equals 1 iff n is in S.
%Y A144315 Cf. A000040, A000043, A000668, A074700, A144313
%K A144315 easy,nonn
%O A144315 1,1
%A A144315 _Reikku Kulon_, Sep 17 2008