A356296 a(n) = Fibonacci(n)^2 mod n.

0, 1, 1, 1, 0, 4, 1, 1, 4, 5, 1, 0, 1, 1, 10, 9, 1, 10, 1, 5, 4, 1, 1, 0, 0, 1, 22, 9, 1, 10, 1, 25, 4, 1, 25, 0, 1, 1, 4, 25, 1, 22, 1, 9, 40, 1, 1, 0, 22, 25, 4, 9, 1, 10, 25, 49, 4, 1, 1, 0, 1, 1, 22, 25, 25, 64, 1, 9, 4, 15, 1, 0, 1, 1, 25, 9, 4, 64, 1, 25, 49, 1, 1, 72, 25, 1

Offset

1,6

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000045(n)^2 mod n.

Maple

A356296 := proc(n)
    modp(combinat[fibonacci](n)^2, n) ;
end proc:
seq(A356296(n), n=1..120) ;

Mathematica

Array[PowerMod[Fibonacci[#], 2, #] &, 86] (* Michael De Vlieger, Aug 03 2022 *)

Prog

(PARI) a(n) = lift(Mod(fibonacci(n), n)^2); \\ Michel Marcus, Aug 03 2022
(Python)
from sympy import fibonacci
def a(n): return pow(fibonacci(n), 2, n)
print([a(n) for n in range(1, 87)]) # Michael S. Branicky, Aug 04 2022

Crossrefs

Cf. A000045, A002708, A023172 (location of zeros), A337231, A337232.

Sequence in context: A176263 A110812 A151904 * A222360 A222371 A222479

Adjacent sequences: A356293 A356294 A356295 * A356297 A356298 A356299

Keyword

nonn,easy

Author

R. J. Mathar, Aug 03 2022

Status

approved