A003893 -id:A003893 - cp's OEIS frontend

A264763 a(0) = a(1) = 1; for n>1, a(n) = a(n-1) + (a(n-2) mod 5).

1, 1, 2, 3, 5, 8, 8, 11, 14, 15, 19, 19, 23, 27, 30, 32, 32, 34, 36, 40, 41, 41, 42, 43, 45, 48, 48, 51, 54, 55, 59, 59, 63, 67, 70, 72, 72, 74, 76, 80, 81, 81, 82, 83, 85, 88, 88, 91, 94, 95, 99, 99, 103, 107, 110, 112, 112

Offset: 0

Anders Hellström, Nov 23 2015

Cf. A000045, A003893.

[n le 2 select 1 else Self(n-1)+Self(n-2) mod 5: n in [1..60]]; // Vincenzo Librandi, Nov 24 2015

a[0] = a[1] = 1; a[n_] := a[n] = a[n - 1] + Mod[a[n - 2], 5]; Table[a@ n, {n, 0, 60}] (* Michael De Vlieger, Nov 24 2015 *)

first(m)=my(v=vector(m));v[1]=1;v[2]=1;for(i=3,m,v[i]=v[i-1]+v[i-2]%5);v

Empirical g.f.: (4*x^12+2*x^11-2*x^10-2*x^9+4*x^8+x^7-2*x^6+x^5+2*x^4+x^3+1) / ((x-1)^2*(x^4+x^3+x^2+x+1)*(x^8-x^6+x^4-x^2+1)). - Colin Barker, Nov 23 2015

A287533 Fibonacci numbers modulo 20.

Original entry on oeis.org

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

Alonso del Arte, May 26 2017

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.

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).

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

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

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

cp's OEIS Frontend

A264763 a(0) = a(1) = 1; for n>1, a(n) = a(n-1) + (a(n-2) mod 5).

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