

A217853


Fermat pseudoprimes to base 3 of the form (3^(4*k + 2)  1)/8.


2



91, 7381, 597871, 48427561, 3922632451, 317733228541, 25736391511831, 2084647712458321, 168856464709124011, 1107867264956562636991, 588766087155780604365200461, 47690053059618228953581237351, 25344449488056571213320166359119221, 166284933091139163730593611482181209801
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

These numbers were obtained for values of k from 1 to 20, with the following exceptions: k = 10, 12, 13, 16, 17, 19, for which were obtained 3^n mod n = 3^7, 3^31, 3^37, 3^25, 3^31, 3^13.
Conjecture: There are infinitely many Fermat pseudoprimes to base 3 of the form (3^(4*k + 2)  1)/8, where k is a natural number.
It is true: for example, when 2k+1 is a prime number (see A210461).  Bruno Berselli, Jan 22 2013


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..190
Eric Weisstein's World of Mathematics, Fermat Pseudoprime


MATHEMATICA

Select[Table[(3^(4k + 2)  1)/8, {k, 80}], PowerMod[3, #  1, #] == 1 &] (* Alonso del Arte, May 14 2019 *)


PROG

(PARI) list(lim)=my(v=List(), t); lim\=1; for(k=1, (logint(8*lim+1, 3)2)\4, t=3^(4*k + 2)>>3; if(Mod(3, t)^t==3, listput(v, t))); Vec(v) \\ Charles R Greathouse IV, Jun 30 2017


CROSSREFS

Cf. A005935, A210461 (subsequence), A217841.
Sequence in context: A234123 A103855 A238541 * A210461 A022253 A172174
Adjacent sequences: A217850 A217851 A217852 * A217854 A217855 A217856


KEYWORD

nonn


AUTHOR

Marius Coman, Oct 12 2012


STATUS

approved



