

A337625


Odd composite integers m such that F(m)^2 == 1 (mod m) and L(m) == 1 (mod m), where F(m) and L(m) are the mth Fibonacci and Lucas numbers, respectively.


4



2737, 4181, 5777, 6721, 10877, 13201, 15251, 29281, 34561, 51841, 64079, 64681, 67861, 68251, 75077, 80189, 90061, 96049, 97921, 100127, 105281, 113573, 118441, 146611, 161027, 162133, 163081, 179697, 186961, 194833, 197209, 219781, 228241, 231703, 252601, 254321
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OFFSET

1,1


COMMENTS

These numbers may be called weak generalized FibonacciLucasBruckner pseudoprimes.
If p is a prime, then F(p)^2 == 1 (mod p) and L(p) == 1 (mod p).
This sequence contains the odd composite integers for which these congruences hold.
For a,b integers, the following sequences are defined:
generalized Lucas sequences by U(n+2)=a*U(n+1)b*U(n) and U(0)=0, U(1)=1,
generalized PellLucas sequences by V(n+2)=a*V(n+1)b*V(n) and V(0)=2, V(1)=a.
These satisfy the identities U(p)^2 == 1 and V(p)==a (mod p) for p prime and b=1,1.
These numbers may be called weak generalized LucasBruckner pseudoprimes of parameters a and b.The current sequence is defined for a=1 and b=1.
Examples: a(n) is also the number of Jones graphs on n nodes.


LINKS



MATHEMATICA

Select[Range[3, 20000, 2], CompositeQ[#] && Divisible[Fibonacci[#, 1]*Fibonacci[#, 1]  1, #] && Divisible[LucasL[#, 1]  1, #] &]


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



