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 A337237 Odd composite integers such that A052918(m-1)^2 == 1 (mod m). 4
 9, 15, 25, 27, 35, 45, 65, 75, 91, 121, 135, 143, 175, 225, 275, 325, 385, 455, 533, 595, 615, 675, 935, 1035, 1107, 1325, 1359, 1431, 1495, 1547, 1573, 1935, 2015, 2255, 2275, 2775, 3025, 3059, 3575, 3605, 4025, 4081, 4235, 4355, 5005, 5089, 5475, 5525, 5719, 5993, 6165 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If p is a prime, then A052918(p-1)^2 == 1 (mod p). This sequence contains the odd composite integers for which the congruence holds. The generalized Lucas sequence of integer parameters (a,b) defined by U(n+2) = a*U(n+1)-b*U(n) and U(0)=0, U(1)=1, satisfies the identity U^2(p) == 1 (mod p) whenever p is prime and b=-1,1 (this property is a form of pseudoprimality). For a=5, b=-1, U(n) recovers A052918(n-1), for n=1,2,.... REFERENCES D. Andrica, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (to appear, 2020) D. Andrica, O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, Mediterr. J. Math. (to appear, 2021) LINKS Amiram Eldar, Table of n, a(n) for n = 1..1000 Dorin Andrica and Ovidiu Bagdasar, On Generalized Lucas Pseudoprimality of Level k, Mathematics (2021) Vol. 9, 838. MATHEMATICA Select[Range[3, 20000, 2], CompositeQ[#] && Divisible[Fibonacci[#, 5]*Fibonacci[#, 5] - 1, #] &] CROSSREFS Cf. A337231 (a=1, odd terms), A337232 (a=1, even terms), A337233 (a=2), A337234 (a=3, odd terms), A337235 (a=3, even terms), A337236 (a=4). Sequence in context: A164384 A138193 A330947 * A036315 A340120 A020154 Adjacent sequences: A337234 A337235 A337236 * A337238 A337239 A337240 KEYWORD nonn AUTHOR Ovidiu Bagdasar, Aug 20 2020 STATUS approved

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Last modified September 28 23:23 EDT 2023. Contains 365739 sequences. (Running on oeis4.)