# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a335674 Showing 1-1 of 1 %I A335674 #16 Nov 23 2023 11:47:41 %S A335674 15,21,35,105,161,195,255,345,385,399,465,527,551,609,741,897,1105, %T A335674 1295,1311,1807,1919,2001,2015,2071,2085,2121,2415,2737,2915,3289, %U A335674 3815,4031,4033,4355,4879,4991,5291,5777,5983,6049,6061,6083,6479,6601,6785,7645,7905,8695,8855,8911,9361,9591,9889 %N A335674 Odd composite integers m such that A003501(m) == 5 (mod m). %C A335674 If p is a prime, then A003501(p)==5 (mod p). %C A335674 This sequence contains the odd composite integers for which the congruence holds. %C A335674 The generalized Pell-Lucas sequences of integer parameters (a,b) defined by V(n+2)=a*V(n+1)-b*V(n) and V(0)=2, V(1)=a, satisfy the identity V(p)==a (mod p) whenever p is prime and b=-1,1. %C A335674 For a=5, b=1, V(n) recovers A003501(n). %D A335674 D. Andrica, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (to appear, 2020). %H A335674 Chai Wah Wu, Table of n, a(n) for n = 1..1000 %H A335674 D. Andrica and O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, preprint for Mediterr. J. Math. 18, 47 (2021). %e A335674 15 is the first odd composite integer for which the relation A003501(15)=16098445550==5 (mod 15) holds. %t A335674 Select[Range[3, 5000, 2], CompositeQ[#] && Divisible[2*ChebyshevT[#, 5/2] - 5, #] &] (* _Amiram Eldar_, Jun 18 2020 *) %Y A335674 Cf. A005248, A335669 (a=3,b=-1), A335672 (a=3,b=1), A335673 (a=4,b=1). %K A335674 nonn %O A335674 1,1 %A A335674 _Ovidiu Bagdasar_, Jun 17 2020 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE