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

0,4

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]

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).

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 *)

Prog

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

Crossrefs

Cf. A000045, A001175, A105870,

Sequence in context: A152909 A328597 A118604 * A287533 A072123 A135102

Adjacent sequences: A261691 A261692 A261693 * A261695 A261696 A261697

Keyword

nonn,easy

Author

G. C. Greubel, Nov 18 2015

Status

approved