cp's OEIS Frontend

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.

%I A141137 #25 Jul 16 2021 03:26:00
%S A141137 8539786,12813274,17340938,33940178,64132426,89733106,95173786,
%T A141137 187473826,203211098,234735586,353686906,799171066,919831058,
%U A141137 1188287794,1955272906,2166139898,2309861746,2864860298,3871638242,5313594466,5867301826
%N 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.
%C A141137 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.
%C A141137 a(69) > 2.6 * 10^11. - _Dana Jacobsen_, May 25 2015
%H A141137 Dana Jacobsen, <a href="/A141137/b141137.txt">Table of n, a(n) for n = 1..68</a>
%H A141137 Dorin Andrica and Ovidiu Bagdasar, <a href="https://doi.org/10.1007/978-3-030-51502-7">Recurrent Sequences: Key Results, Applications, and Problems</a>, Springer (2020), p. 88.
%H A141137 Dorin Andrica and Ovidiu Bagdasar, <a href="https://doi.org/10.3390/math9080838">On Generalized Lucas Pseudoprimality of Level k</a>, Mathematics (2021) Vol. 9, 838.
%o A141137 (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
%Y A141137 Cf. A081264.
%K A141137 nice,nonn
%O A141137 1,1
%A A141137 _T. D. Noe_, Jun 09 2008
%E A141137 a(19) from _Giovanni Resta_, Jul 20 2013
%E A141137 a(20)-a(21) from _Dana Jacobsen_, May 25 2015