# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a281576 Showing 1-1 of 1 %I A281576 #51 Jul 24 2021 04:25:00 %S A281576 4294967297,18446744073709551617, %T A281576 340282366920938463463374607431768211457, %U A281576 115792089237316195423570985008687907853269984665640564039457584007913129639937 %N A281576 Composite Fermat numbers. %C A281576 Complement of A019434 in A000215. %C A281576 Intersection of A000215 and A002808. %C A281576 Fermat numbers F_i such that A152155(i) != -1, where i is the index of F in A000215. %C A281576 Is this sequence infinite? %C A281576 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 A281576 Giuseppe Coppoletta, Table of n, a(n) for n = 1..7 %H A281576 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. %H A281576 Samuel S. Wagstaff, The Cunningham Project, Complete factoring status (compiled by Wilfrid Keller). %o A281576 (PARI) a152155(n) = centerlift(Mod(3, 2^(2^n)+1)^(2^(2^n-1))) %o A281576 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 A281576 terms(4) \\ print initial 4 terms %Y A281576 Cf. A000215, A001567, A002808, A019434, A046052. %K A281576 nonn %O A281576 1,1 %A A281576 _Felix Fröhlich_, Jan 24 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE