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 A340240 Odd composite integers m such that A004254(3*m-J(m,21)) == 5*J(m,21) (mod m) and gcd(m,21)=1, where J(m,21) is the Jacobi symbol. 2
 55, 407, 527, 529, 551, 559, 965, 1199, 1265, 1633, 1807, 1919, 1961, 3401, 3959, 4033, 4381, 5461, 5777, 5977, 5983, 6049, 6233, 6439, 6479, 7141, 7195, 7645, 7999, 8639, 8695, 8993, 9265, 9361, 11663, 11989, 12209, 12265, 13019, 13021, 13199, 14023, 14465, 14491 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The generalized Lucas sequences of integer parameters (a,b) defined by U(m+2)=a*U(m+1)-b*U(m) and U(0)=0, U(1)=1, satisfy U(3*p-J(p,D)) == a*J(p,D) (mod p) whenever p is prime, k is a positive integer, b=1 and D=a^2-4. The composite integers m with the property U(k*m-J(m,D)) == U(k-1)*J(m,D) (mod m) are called generalized Lucas pseudoprimes of level k+ and parameter a. Here b=1, a=5, D=21 and k=3, while U(m) is A004254(m). REFERENCES D. Andrica, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer, 2020. D. Andrica, O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, Mediterr. J. Math. (to appear, 2021). D. Andrica, O. Bagdasar, On generalized pseudoprimality of level k (submitted). LINKS Table of n, a(n) for n=1..44. Dorin Andrica, Vlad Crişan, and Fawzi Al-Thukair, On Fibonacci and Lucas sequences modulo a prime and primality testing, Arab Journal of Mathematical Sciences, 2018, 24(1), 9--15. MATHEMATICA Select[Range[3, 15000, 2], CoprimeQ[#, 21] && CompositeQ[#] && Divisible[ ChebyshevU[3*# - JacobiSymbol[#, 21] - 1, 5/2] - 5*JacobiSymbol[#, 21], #] &] CROSSREFS Cf. A004254, A071904, A340098 (a=5, b=1, k=1), A340123 (a=5, b=1, k=2). Cf. A340239 (a=3, b=1, k=3), A340241 (a=7, b=1, k=3). Sequence in context: A063653 A222348 A075740 * A355511 A129217 A116060 Adjacent sequences: A340237 A340238 A340239 * A340241 A340242 A340243 KEYWORD nonn AUTHOR Ovidiu Bagdasar, Jan 01 2021 STATUS approved

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Last modified September 12 15:43 EDT 2024. Contains 375853 sequences. (Running on oeis4.)