cp's OEIS Frontend

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.

A152121 a(0) = 4; for n>0, a(n) = a(n-1)^2 - 2^(1+2^(n-1)).

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%I A152121 #5 Jun 02 2025 01:12:54
%S A152121 4,12,136,18464,340918784,116225617283907584,
%T A152121 13508394113025357323362163662782464,
%U A152121 182476711512818130204254420972394401125552102555370860811711166808064
%N A152121 a(0) = 4; for n>0, a(n) = a(n-1)^2 - 2^(1+2^(n-1)).
%C A152121 A subset of A056236, where a(n) = (2+sqrt(2))^n+(2-sqrt(2))^n, when the exponent n is a nonnegative integer power of 2. I.E.: a(0) = (2+sqrt(2))^(2^0)+(2-sqrt(2))^(2^0), a(1) = (2+sqrt(2))^(2^1)+(2-sqrt(2))^(2^1); a(2) = (2+sqrt(2))^(2^2)+(2-sqrt(2))^(2^2); etc.
%C A152121 For all n the value 2^(n+1) can be factored from each a(n), which except for a different initial term (a(0) = 2 instead of a(0) = 1) matches the sequence A001601 for n>0.
%H A152121 Dennis Martin, <a href="/A152121/b152121.txt">Table of n, a(n) for n = 0..10</a>
%F A152121 a(n) = a(n-1)^2 - 2^(1+2^(n-1))
%e A152121 a(0) = 4; a(1) = 4^2 - 2^2 = 12; a(2) = 12^2 - 2^3 = 136; a(3) = 136^2 - 2^5 = 18464; a(4) = 18464^2 - 2^9 = 340918784.
%Y A152121 Cf. A056236, A001601
%K A152121 easy,nonn
%O A152121 0,1
%A A152121 Dennis Martin (dennis.martin(AT)dptechnology.com), Nov 24 2008