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

Author

R. J. Mathar, Aug 03 2022

Keywords

• nonn
• easy

Links

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

Crossrefs

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

Programs

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 *)

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

Formula

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