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 A190840 #79 Apr 27 2023 16:48:26 %S A190840 1,8,288,332928,443365544448,786292024016459316676608, %T A190840 2473020588127600939387543243786675530709484249088 %N A190840 a(n+1) = 4*a(n)*(a(n)+1) for a(0) = 1. %C A190840 For n>0, subsequence of A132592: both a(n)/2 and a(n)+1 are squares. %C A190840 All terms (n > 0) are divisible by 8, yielding all terms of A185097, which is indexed from n=1, thus having the first term A185097(1) = 1. %C A190840 The next term has 98 digits. - _Harvey P. Dale_, Jan 01 2014 %C A190840 For n>0, subsequence of A060355: both a(n) and a(n)+1 are powerful numbers. - _Bernard Schott_, Apr 24 2023 %F A190840 a(n+1) = 4*a(n)*(a(n)+1) for a(0) = 1. %F A190840 a(n) = sinh(2^(n-2)*arccosh(17))^2. - _Alexander R. Povolotsky_, Aug 14 2011 %F A190840 a(n) = 8*A185097(n) for n > 0. - _Alexander R. Povolotsky_, Aug 14 2011 %F A190840 a(n) = (1 + sqrt(2))^(2^(n+1))/4 + (1 - sqrt(2))^(2^(n+1))/4 - 1/2. Therefore 2*a(n) + 1 = A001601(n+1). - _Bruno Berselli_, Feb 01 2017 %t A190840 NestList[4#(#+1)&,1,7] (* _Harvey P. Dale_, Jan 01 2014 *) %Y A190840 Cf. A000217, A001601, A060355, A132592, A185097. %K A190840 nonn %O A190840 0,2 %A A190840 _Alexander Zhukov_, Aug 08 2011