A261694 a(n) = Fibonacci(n) mod 21.

0, 1, 1, 2, 3, 5, 8, 13, 0, 13, 13, 5, 18, 2, 20, 1, 0, 1, 1, 2, 3, 5, 8, 13, 0, 13, 13, 5, 18, 2, 20, 1, 0, 1, 1, 2, 3, 5, 8, 13, 0, 13, 13, 5, 18, 2, 20, 1, 0, 1, 1, 2, 3, 5, 8, 13, 0, 13, 13, 5, 18, 2, 20, 1, 0, 1, 1, 2, 3, 5, 8, 13, 0, 13, 13, 5, 18, 2, 20, 1, 0, 1, 1, 2, 3, 5, 8, 13, 0, 13

Offset: 0

Author

G. C. Greubel, Nov 18 2015

Keywords

• nonn
• easy

Comments

Sequence is periodic with Pisano period 16; Pisano number 21 in the sequence A001175. The only other sequence with Pisano period 16 is that of A105870 which is the Fibonacci sequence mod 7. This is Pisano number 7.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000 [a(391) = 13 corrected by _Georg Fischer_, May 24 2019]

Crossrefs

Cf. A000045, A001175, A105870,

Programs

Magma

[Fibonacci(n) mod 21: n in [0..120]]; // Vincenzo Librandi, Nov 19 2015

Mathematica

Table[Mod[Fibonacci[n], 21], {n, 0, 100}]
PadRight[{},120,{0,1,1,2,3,5,8,13,0,13,13,5,18,2,20,1}] (* Harvey P. Dale, May 16 2020 *)

PARI

a(n) = fibonacci(n)%21; \\ Altug Alkan, Nov 19 2015

Python

A261694_list, a, b, = [], 0, 1
for _ in range(10**3):
    A261694_list.append(a)
    a, b = b, (a+b) % 21 # Chai Wah Wu, Nov 26 2015

Formula

G.f.: x*(1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 8*x^5 + 13*x^6 + 13*x^8 + 13*x^9 + 5*x^10 + 18*x^11 + 2*x^12 + 20*x^13 + x^14)/(1-x^16).