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 A338311 Even composites m such that A003499(m)==6 (mod m). 1
 4, 14, 28, 164, 434, 574, 1106, 5084, 5572, 7874, 8386, 13454, 13694, 19964, 21988, 33166, 39934, 40132, 95122, 103886, 113918, 148994, 157604, 215326, 216124, 256004, 277564, 306404, 341342, 366148, 571154, 660674, 662494, 764956, 771374, 876644, 981646, 1070926 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If p is a prime, then A003499(p)==6 (mod p). This sequence contains the even composite integers for which the congruence holds. The generalized Pell-Lucas sequence of integer parameters (a,b) defined by V(m+2)=a*V(m+1)-b*V(m) and V(0)=2, V(1)=a, satisfy the identity V(p)==a (mod p) whenever p is prime and b=-1,1. For a=6 and b=1, V(m) recovers A003499(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) LINKS MATHEMATICA Select[Range[2, 25000, 2], CompositeQ[#] && Divisible[2*ChebyshevT[#, 3] - 6, #] &] CROSSREFS Cf. A337233 (sequence of odd terms), A337777 (a=3). Sequence in context: A033690 A316213 A296985 * A244714 A218212 A305637 Adjacent sequences: A338308 A338309 A338310 * A338312 A338313 A338314 KEYWORD nonn AUTHOR Ovidiu Bagdasar, Oct 22 2020 EXTENSIONS More terms from Amiram Eldar, Oct 22 2020 STATUS approved

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Last modified March 21 07:53 EDT 2023. Contains 361393 sequences. (Running on oeis4.)