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 A112714 #22 Aug 15 2025 15:57:16
%S A112714 1,3,7,11,15,23,31,39,47,55,63,79,95,111,127,143,159,175,191,207,223,
%T A112714 239,255,287,319,351,383,415,447,479,511,543,575,607,639,671,703,735,
%U A112714 767,799,831,863,895,927,959,991,1023,1087,1151,1215,1279,1343,1407
%N A112714 Numbers of the form k*2^m-1 with k<2^m and k odd.
%H A112714 Robert Israel, <a href="/A112714/b112714.txt">Table of n, a(n) for n = 1..10000</a>
%H A112714 Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, <a href="https://arxiv.org/abs/2210.10968">Identities and periodic oscillations of divide-and-conquer recurrences splitting at half</a>, arXiv:2210.10968 [cs.DS], 2022, p. 38.
%H A112714 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ProthNumber.html">Proth Numbers</a>
%F A112714 a(n) = A080075(n)-2. - _Thomas Ordowski_, Aug 15 2025
%e A112714 a(4)=7 because 7 = 1*2^3 - 1, with 1 < 2^3, and it is the fourth number of this form.
%p A112714 N:= 2000: # to get all terms <= N
%p A112714 sort(convert({seq(seq(k*2^m-1,k=1..min((N+1)/2^m,2^m-1),2),m=1..ilog2(N+1))},list)); # _Robert Israel_, May 23 2017
%t A112714 Take[Sort@Flatten@Table[k*2^m - 1, {m, 0, 10}, {k, 1, 2^m - 1, 2}], 53] (* _Robert G. Wilson v_, Jan 02 2006 *)
%o A112714 (PARI) for(n=2,8,for(k=2^(n-2)+1,2^n,print1(k*2^n-1","))) \\ Note that the first two terms (1,3) are not computed
%Y A112714 Cf. A080075.
%K A112714 easy,nonn
%O A112714 1,2
%A A112714 Jose Brox (tautocrona(AT)terra.es), Dec 31 2005