%I #51 Jul 24 2021 04:25:00

%S 4294967297,18446744073709551617,

%T 340282366920938463463374607431768211457,

%U 115792089237316195423570985008687907853269984665640564039457584007913129639937

%N Composite Fermat numbers.

%C Complement of A019434 in A000215.

%C Intersection of A000215 and A002808.

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

%C Is this sequence infinite?

%C 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

%H Giuseppe Coppoletta, <a href="/A281576/b281576.txt">Table of n, a(n) for n = 1..7</a>

%H John H. Jaroma and Kamaliya N. Reddy, <a href="https://www.jstor.org/stable/27642303">Classical and alternative approaches to the Mersenne and Fermat numbers</a>, The American Mathematical Monthly, Vol. 114, No. 8 (2007), pp. 677-687.

%H Samuel S. Wagstaff, <a href="http://www.prothsearch.com/fermat.html">The Cunningham Project, Complete factoring status (compiled by Wilfrid Keller)</a>.

%o (PARI) a152155(n) = centerlift(Mod(3, 2^(2^n)+1)^(2^(2^n-1)))

%o terms(n) = my(i=0, k=1); while(1, if(a152155(k)!=-1, print1(2^(2^k)+1, ", "); i++); if(i==n, break); k++)

%o terms(4) \\ print initial 4 terms

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

%K nonn

%O 1,1

%A _Felix Fröhlich_, Jan 24 2017