A281576 Composite Fermat numbers.

4294967297, 18446744073709551617, 340282366920938463463374607431768211457, 115792089237316195423570985008687907853269984665640564039457584007913129639937

Offset: 1

Author

Felix Fröhlich, Jan 24 2017

Keywords

• nonn

Comments

Complement of A019434 in A000215.

Intersection of A000215 and A002808.

Fermat numbers F_i such that A152155(i) != -1, where i is the index of F in A000215.

Is this sequence infinite?

All the terms are Fermat pseudoprimes to base 2 (A001567). For a proof see, e.g., Jaroma and Reddy (2007). - Amiram Eldar, Jul 24 2021

Links

• Giuseppe Coppoletta, Table of n, a(n) for n = 1..7
• John H. Jaroma and Kamaliya N. Reddy, Classical and alternative approaches to the Mersenne and Fermat numbers, The American Mathematical Monthly, Vol. 114, No. 8 (2007), pp. 677-687.
• Samuel S. Wagstaff, The Cunningham Project, Complete factoring status (compiled by Wilfrid Keller).

Crossrefs

Cf. A000215, A001567, A002808, A019434, A046052.

Programs

PARI

a152155(n) = centerlift(Mod(3, 2^(2^n)+1)^(2^(2^n-1)))
terms(n) = my(i=0, k=1); while(1, if(a152155(k)!=-1, print1(2^(2^k)+1, ", "); i++); if(i==n, break); k++)
terms(4) \\ print initial 4 terms