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

Author

T. D. Noe, Jun 09 2008

Keywords

• nice
• nonn

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.

Crossrefs

Cf. A081264.

Programs

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

Extensions

a(19) from Giovanni Resta, Jul 20 2013

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