A141137 Even Fibonacci pseudoprimes: even composite numbers k such that either (1) k divides Fibonacci(k-1) if k mod 5 = 1 or -1 or (2) k divides Fibonacci(k+1) if k mod 5 = 2 or -2.

8539786, 12813274, 17340938, 33940178, 64132426, 89733106, 95173786, 187473826, 203211098, 234735586, 353686906, 799171066, 919831058, 1188287794, 1955272906, 2166139898, 2309861746, 2864860298, 3871638242, 5313594466, 5867301826

Offset

1,1

Comments

These even Fibonacci pseudoprimes (FPPs) were found by Kenny Richardson (kenyai(AT)yahoo.com). See A081264 for odd FPPs and references. Be aware that some authors use the term "Fibonacci pseudoprime" for pseudoprimes in Lucas sequences. For example, see A005845 for Lucas V(1,-1) pseudoprimes.

a(69) > 2.6 * 10^11. - Dana Jacobsen, May 25 2015

Links

Dana Jacobsen, Table of n, a(n) for n = 1..68

Dorin Andrica and Ovidiu Bagdasar, Recurrent Sequences: Key Results, Applications, and Problems, Springer (2020), p. 88.

Dorin Andrica and Ovidiu Bagdasar, On Generalized Lucas Pseudoprimality of Level k, Mathematics (2021) Vol. 9, 838.

Prog

(Perl) use ntheory ":all"; for (3..1e10) { my $n = $_<<1; $e = (0, -1, 1, 1, -1)[$n%5]; next unless $e; say $n unless (lucas_sequence($n, 1, -1, $n+$e))[0]; } # Dana Jacobsen, May 25 2015

Crossrefs

Cf. A081264.

Sequence in context: A251173 A203824 A081639 * A184150 A236450 A237074

Adjacent sequences: A141134 A141135 A141136 * A141138 A141139 A141140

Keyword

nice,nonn

Author

T. D. Noe, Jun 09 2008

Extensions

a(19) from Giovanni Resta, Jul 20 2013

a(20)-a(21) from Dana Jacobsen, May 25 2015

Status

approved