A338079 Odd composite integers m such that A086902(m) == 7 (mod m).

25, 51, 91, 161, 265, 325, 425, 561, 791, 1105, 1113, 1325, 1633, 1921, 1961, 2001, 2465, 2599, 2651, 2737, 3445, 4081, 4505, 4929, 7345, 7685, 8449, 9361, 10325, 10465, 10825, 11285, 11713, 12025, 12291, 13021, 15457, 17111, 18193, 18881, 18921, 19307

Offset

1,1

Comments

If p is a prime, then A086902(p)==7 (mod p).

This sequence contains the odd 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=7, b=-1, V(m) recovers A086902(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

Table of n, a(n) for n=1..42.

Mathematica

Select[Range[3, 20000, 2], CompositeQ[#] && Divisible[LucasL[#, 7] - 7, #] &]

Crossrefs

Cf. A006497, A005845 (a=1), A330276 (a=2), A335669 (a=3), A335670 (a=4), A335671 (a=5), A338078 (a=6).

Sequence in context: A042234 A042232 A273868 * A337630 A270693 A042240

Adjacent sequences: A338076 A338077 A338078 * A338080 A338081 A338082

Keyword

nonn

Author

Ovidiu Bagdasar, Oct 08 2020

Status

approved