A002716 -id:A002716 - cp's OEIS frontend

A220294 a(n) = 1 - 2^(2^n) + 2^(2^(n+1)).

3, 13, 241, 65281, 4294901761, 18446744069414584321, 340282366920938463444927863358058659841, 115792089237316195423570985008687907852929702298719625575994209400481361428481

Offset: 0

Michael Somos, Dec 10 2012

nonn

An infinite coprime sequence defined by recursion.

Cf. A001146, A002061, A002716, A087046, A111403, A220161, A255770, A255771, A255772.

[1 - 2^(2^n) + 2^(2^(n+1)): n in [0..10]]; // G. C. Greubel, Aug 10 2018

Table[4^(2^m) - 2^(2^m) + 1, {m, 0, 7}] (* Michael De Vlieger, Aug 02 2016 *)

A220294(n):=1 - 2^(2^n) + 2^(2^(n+1))$ makelist(A220294(n),n,0,10); /* Martin Ettl, Dec 10 2012 */

{a(n) = if( n<0, 0, 1 - 2^(2^n) + 2^(2^(n+1)))};

A220161(n+1) = a(n) * A220161(n).
a(n+1) = 1 + (a(n) - 1) * (A220161(n) - 1).
a(n) = A002716(2*n) = 1 + A087046(n+2) = 1 + A111403(n).
a(n) = A002061(A001146(n)). - Pontus von Brömssen, Aug 31 2021

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

Original entry on oeis.org

2, 12, 240, 65280, 4294901760, 18446744069414584320, 340282366920938463444927863358058659840, 115792089237316195423570985008687907852929702298719625575994209400481361428480

Offset: 0

N. J. A. Sloane, Nov 12 2005

nonn

			The binary representation of the first values shows what is going on:
10
1100
11110000
1111111100000000
11111111111111110000000000000000
...

Alois P. Heinz, Table of n, a(n) for n = 0..10

Probably equal to A087046(n+2). Doubled A040996.

a:= n-> (p-> p*(p-1))(2^(2^n)):
seq(a(n), n=0..7);  # Alois P. Heinz, Jan 03 2018

Conjecture: a(n) = A002716(2*n)-1. - R. J. Mathar, May 15 2007
From Alois P. Heinz, Jan 03 2018: (Start)
a(n) = 2^(2*2^n) - 2^(2^n).
a(n) = p*(p-1) with p = 2^(2^n). (End)
a(n) = A040996(n) * 2. - Tilman Piesk, Oct 04 2024

Example and cross-reference from Olivier Gérard, Jun 23 2014

cp's OEIS Frontend

A220294 a(n) = 1 - 2^(2^n) + 2^(2^(n+1)).

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

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