A335674 - OEIS

A335674

Odd composite integers m such that A003501(m) == 5 (mod m).

15, 21, 35, 105, 161, 195, 255, 345, 385, 399, 465, 527, 551, 609, 741, 897, 1105, 1295, 1311, 1807, 1919, 2001, 2015, 2071, 2085, 2121, 2415, 2737, 2915, 3289, 3815, 4031, 4033, 4355, 4879, 4991, 5291, 5777, 5983, 6049, 6061, 6083, 6479, 6601, 6785, 7645, 7905, 8695, 8855, 8911, 9361, 9591, 9889

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OFFSET

1,1

COMMENTS

If p is a prime, then A003501(p)==5 (mod p).

This sequence contains the odd composite integers for which the congruence holds.

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.

For a=5, b=1, V(n) recovers A003501(n).

REFERENCES

D. Andrica, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (to appear, 2020).

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..1000

D. Andrica and O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, preprint for Mediterr. J. Math. 18, 47 (2021).

EXAMPLE

15 is the first odd composite integer for which the relation A003501(15)=16098445550==5 (mod 15) holds.

MATHEMATICA

Select[Range[3, 5000, 2], CompositeQ[#] && Divisible[2*ChebyshevT[#, 5/2] - 5, #] &] (* Amiram Eldar, Jun 18 2020 *)

CROSSREFS

Cf. A005248, A335669 (a=3,b=-1), A335672 (a=3,b=1), A335673 (a=4,b=1).

Sequence in context: A081977 A180655 A254365 * A349096 A063175 A367103

Adjacent sequences: A335671 A335672 A335673 * A335675 A335676 A335677

KEYWORD

nonn

AUTHOR

Ovidiu Bagdasar, Jun 17 2020

STATUS

approved