A217841 -id:A217841 - cp's OEIS frontend

A217853 Fermat pseudoprimes to base 3 of the form (3^(4*k + 2) - 1)/8.

91, 7381, 597871, 48427561, 3922632451, 317733228541, 25736391511831, 2084647712458321, 168856464709124011, 1107867264956562636991, 588766087155780604365200461, 47690053059618228953581237351, 25344449488056571213320166359119221, 166284933091139163730593611482181209801

Offset: 1

Marius Coman, Oct 12 2012

nonn

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

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

Cf. A005935, A210461 (subsequence), A217841.

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

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

cp's OEIS Frontend

A217853 Fermat pseudoprimes to base 3 of the form (3^(4*k + 2) - 1)/8.

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