A338081 - OEIS

%I #10 Jul 08 2021 23:24:44

%S 21,25,35,49,51,65,85,91,119,147,161,175,221,231,245,325,357,377,391,

%T 399,425,455,539,559,561,575,595,629,637,759,791,833,1001,1105,1127,

%U 1225,1247,1295,1309,1495,1547,1633,1763,1775,1921,2001,2015,2261,2275,2407

%N Odd composite integers such that A054413(m)^2 == 1 (mod m).

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

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

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

%C 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).

%D D. Andrica, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer, 2020.

%D D. Andrica, O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, Mediterr. J. Math. (to appear, 2021)

%H Dorin Andrica and Ovidiu Bagdasar, <a href="https://doi.org/10.3390/math9080838">On Generalized Lucas Pseudoprimality of Level k</a>, Mathematics (2021) Vol. 9, 838.

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

%Y 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).

%K nonn

%O 1,1

%A _Ovidiu Bagdasar_, Oct 08 2020