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 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 m-th 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Intersection of A005845 and A337231. These numbers may be called weak generalized Fibonacci-Lucas-Bruckner 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 Pell-Lucas 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 Lucas-Bruckner 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 Table of n, a(n) for n=1..36. Dorin Andrica and Ovidiu Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, Mediterr. J. Math., 18 (2021), 47. MATHEMATICA Select[Range[3, 20000, 2], CompositeQ[#] && Divisible[Fibonacci[#, 1]*Fibonacci[#, 1] - 1, #] && Divisible[LucasL[#, 1] - 1, #] &] CROSSREFS Cf. A005845 and A337231. Sequence in context: A253987 A258904 A221976 * A094401 A035774 A107570 Adjacent sequences: A337622 A337623 A337624 * A337626 A337627 A337628 KEYWORD nonn AUTHOR Ovidiu Bagdasar, Sep 19 2020 EXTENSIONS More terms from Amiram Eldar, Sep 19 2020 STATUS approved

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Last modified November 30 12:38 EST 2023. Contains 367461 sequences. (Running on oeis4.)