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 A126883 #25 Jul 09 2024 15:57:36 %S A126883 0,1,7,63,1023,32767,2097151,268435455,68719476735,35184372088831, %T A126883 36028797018963967,73786976294838206463,302231454903657293676543, %U A126883 2475880078570760549798248447,40564819207303340847894502572031,1329227995784915872903807060280344575 %N A126883 a(n) = (2^0)*(2^1)*(2^2)*(2^3)...(2^n)-1 = 2^T(n) - 1 where T(n) = A000217(n) is the n-th triangular number. %C A126883 For n > 2, a(n) and a(n-1) share at least one prime factor. %C A126883 Shows how many patterns can be created with 1-color thread while sewing on a button with buttonholes located on the vertices of a convex n-gon. - _Ivan N. Ianakiev_, Feb 09 2012 %D A126883 Masha Gessen, Perfect Rigor, A Genius and the Mathematical Breakthrough of the Century, Houghton Mifflin Harcourt, 2009, page 38. %H A126883 Muniru A Asiru, <a href="/A126883/b126883.txt">Table of n, a(n) for n = 0..80</a> %F A126883 a(n) = A006125(n+1) - 1. - _Zerinvary Lajos_, Jun 12 2007 %p A126883 seq(2^(binomial(n+1, 2))-1, n=0..12); # _Zerinvary Lajos_, Jun 12 2007 %t A126883 FoldList[Times,2^Range[0,20]]-1 (* _Harvey P. Dale_, Sep 09 2015 *) %t A126883 2^Accumulate[Range[0,20]]-1 (* _Harvey P. Dale_, Jun 03 2019 *) %o A126883 (GAP) List([-1..15],n->2^(Binomial(2+n,n))-1); # _Muniru A Asiru_, Feb 21 2019 %Y A126883 Cf. A000217, A006125. %K A126883 nonn %O A126883 0,3 %A A126883 _Marco Matosic_, Dec 29 2006 %E A126883 Corrected and extended by _Harvey P. Dale_, Sep 09 2015