A287533 Fibonacci numbers modulo 20.

0, 1, 1, 2, 3, 5, 8, 13, 1, 14, 15, 9, 4, 13, 17, 10, 7, 17, 4, 1, 5, 6, 11, 17, 8, 5, 13, 18, 11, 9, 0, 9, 9, 18, 7, 5, 12, 17, 9, 6, 15, 1, 16, 17, 13, 10, 3, 13, 16, 9, 5, 14, 19, 13, 12, 5, 17, 2, 19, 1, 0, 1, 1, 2, 3, 5, 8, 13, 1, 14, 15, 9, 4, 13, 17, 10, 7, 17, 4, 1

Offset: 0

Author

Alonso del Arte, May 26 2017

Keywords

• nonn
• easy

Comments

Looking at the Fibonacci numbers modulo 10 (A003893), we see their parity and what their least significant digits are in base 10. But it doesn't tell us whether the even Fibonacci numbers are further divisible by 2, nor does it tell us the congruence modulo 4 of the odd Fibonacci numbers.

Modulo 20, the Fibonacci numbers have a period of 60. Aside from 2, 3, 5, Fibonacci primes have a least significant digit of 9, D or J in vigesimal.

Links

• Index entries for linear recurrences with constant coefficients, signature (1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, 1).

Crossrefs

Cf. A079343 (Fibonacci numbers modulo 4), A082116 (Fibonacci numbers modulo 5).

Programs

Mathematica

Mod[Fibonacci[Range[0, 79]], 20]

PARI

a(n)=fibonacci(n%60)%20 \\ Charles R Greathouse IV, Jun 23 2017