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

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

Offset: 0

Author

Michael Somos, Dec 10 2012

Keywords

• nonn

Comments

An infinite coprime sequence defined by recursion.

Crossrefs

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

Programs

Magma

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

Mathematica

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

Maxima

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

PARI

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

Formula

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