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.

A111403 a(n) = f(f(n+1)) - f(f(n)), where f(m) = 2^m.

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%I A111403 #29 Oct 06 2024 09:17:07
%S A111403 2,12,240,65280,4294901760,18446744069414584320,
%T A111403 340282366920938463444927863358058659840,
%U A111403 115792089237316195423570985008687907852929702298719625575994209400481361428480
%N A111403 a(n) = f(f(n+1)) - f(f(n)), where f(m) = 2^m.
%H A111403 Alois P. Heinz, <a href="/A111403/b111403.txt">Table of n, a(n) for n = 0..10</a>
%F A111403 Conjecture: a(n) = A002716(2*n)-1. - _R. J. Mathar_, May 15 2007
%F A111403 From _Alois P. Heinz_, Jan 03 2018: (Start)
%F A111403 a(n) = 2^(2*2^n) - 2^(2^n).
%F A111403 a(n) = p*(p-1) with p = 2^(2^n). (End)
%F A111403 a(n) = A040996(n) * 2. - _Tilman Piesk_, Oct 04 2024
%e A111403 The binary representation of the first values shows what is going on:
%e A111403 10
%e A111403 1100
%e A111403 11110000
%e A111403 1111111100000000
%e A111403 11111111111111110000000000000000
%e A111403 ...
%p A111403 a:= n-> (p-> p*(p-1))(2^(2^n)):
%p A111403 seq(a(n), n=0..7);  # _Alois P. Heinz_, Jan 03 2018
%Y A111403 Probably equal to A087046(n+2). Doubled A040996.
%K A111403 nonn
%O A111403 0,1
%A A111403 _N. J. A. Sloane_, Nov 12 2005
%E A111403 Example and cross-reference from _Olivier Gérard_, Jun 23 2014