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A338314
Even composite integers m such that A004254(m)^2 == 1 (mod m).
0
4, 8, 76, 104, 116, 296, 872, 1112, 1378, 2204, 2774, 2834, 3016, 4472, 5174, 5624, 6364, 6554, 8854, 9164, 9976, 10564, 11026, 11324, 11476, 12644, 14356, 14456, 15124, 15544, 15688, 16484, 20492, 20786, 21944, 26506, 26564, 30302, 31996, 32264, 33368, 35048
OFFSET
1,1
COMMENTS
If p is a prime, then A004254(p)^2 == 1 (mod p).
This sequence contains the even composite integers for which the congruence holds.
The generalized Lucas sequence of integer parameters (a,b) defined by U(m+2) = a*U(m+1)-b*U(m) and U(0)=0, U(1)=1, satisfies the identity U^2(p) == 1 (mod p) whenever p is prime and b=-1,1. For a=5, b=1, U(n) recovers A004254(m).
These numbers may be called weak generalized Lucas pseudoprimes of parameters a and b. The current sequence is defined for a=5 and b=1.
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)
MATHEMATICA
Select[Range[2, 15000, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 5/2]*ChebyshevU[#-1, 5/2] - 1, #] &]
CROSSREFS
Cf. A337782 (a=3), A337783 (a=7).
Sequence in context: A206346 A240503 A221484 * A288956 A353032 A236284
KEYWORD
nonn
AUTHOR
Ovidiu Bagdasar, Oct 22 2020
EXTENSIONS
More terms from Amiram Eldar, Oct 22 2020
STATUS
approved