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A338081 Odd composite integers such that A054413(m)^2 == 1 (mod m). 1
21, 25, 35, 49, 51, 65, 85, 91, 119, 147, 161, 175, 221, 231, 245, 325, 357, 377, 391, 399, 425, 455, 539, 559, 561, 575, 595, 629, 637, 759, 791, 833, 1001, 1105, 1127, 1225, 1247, 1295, 1309, 1495, 1547, 1633, 1763, 1775, 1921, 2001, 2015, 2261, 2275, 2407 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The generalized Lucas sequence of integer parameters (a,b) is defined by

U(m+2) = a*U(m+1)-b*U(m) and U(0)=0, U(1)=1.

Whenever p is prime and b=-1,1 we have U^2(p) == 1 (mod p).

Here we define the odd composite integers for which U^2(m) == 1 (mod m) holds, for a=7, b=-1, where U(m) is A054413(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..50.

MATHEMATICA

Select[Range[3, 15000, 2], CompositeQ[#] && Divisible[Fibonacci[#, 7]*Fibonacci[#, 7] - 1, #] &]

CROSSREFS

Cf. A337231 (a=1, odd terms), A337232 (a=1, even terms), A337233 (a=2), A337234 (a=3, odd terms), A337235 (a=3, even terms), A337236 (a=4), A337237 (a=5),  A338081 (a=6).

Sequence in context: A276700 A181781 A324551 * A118568 A147049 A219393

Adjacent sequences:  A338078 A338079 A338080 * A338082 A338083 A338084

KEYWORD

nonn

AUTHOR

Ovidiu Bagdasar, Oct 08 2020

STATUS

approved

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Last modified May 10 21:08 EDT 2021. Contains 343780 sequences. (Running on oeis4.)