A079343 -id:A079343 - cp's OEIS frontend

A079345 Fibonacci(n) mod 16.

0, 1, 1, 2, 3, 5, 8, 13, 5, 2, 7, 9, 0, 9, 9, 2, 11, 13, 8, 5, 13, 2, 15, 1, 0, 1, 1, 2, 3, 5, 8, 13, 5, 2, 7, 9, 0, 9, 9, 2, 11, 13, 8, 5, 13, 2, 15, 1, 0, 1, 1, 2, 3, 5, 8, 13, 5, 2, 7, 9, 0, 9, 9, 2, 11, 13, 8, 5, 13, 2, 15, 1, 0, 1, 1, 2, 3, 5, 8, 13, 5, 2, 7, 9, 0, 9, 9, 2, 11, 13, 8, 5, 13, 2

Offset: 0

Jon Perry, Jan 04 2003

Periodic with period 24. - Jon Perry, Jan 08 2003

			a(8) = F(8) mod 16 = 21 mod 16 = 5.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Cf. A079343, A079344.

[Fibonacci(n) mod 16: n in [0..100]]; // Vincenzo Librandi, Feb 04 2014

a={};Do[f=Fibonacci[n];AppendTo[a,Mod[f,16]],{n,1,30}];a (* Vladimir Joseph Stephan Orlovsky, Jul 23 2008 *)
Table[Mod[Fibonacci[n], 16], {n, 0, 100}] (* Vincenzo Librandi, Feb 04 2014 *)

for (n=1,100,print1(fibonacci(n)%16","))

A160080 Lodumo_4 of Fibonacci numbers.

Original entry on oeis.org

0, 1, 5, 2, 3, 9, 4, 13, 17, 6, 7, 21, 8, 25, 29, 10, 11, 33, 12, 37, 41, 14, 15, 45, 16, 49, 53, 18, 19, 57, 20, 61, 65, 22, 23, 69, 24, 73, 77, 26, 27, 81, 28, 85, 89, 30, 31, 93, 32, 97, 101, 34, 35, 105, 36, 109, 113, 38, 39, 117, 40, 121, 125, 42, 43, 129, 44, 133, 137, 46

Offset: 0

Philippe Deléham, May 01 2009

Permutation of nonnegative numbers.

OEIS wiki, Lodumo transform
Index entries for sequences that are permutations of the nonnegative integers
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,2,0,0,0,0,0,-1).

Cf. A004767, A008586, A016825, A017533, A017581, A017629, A079343.

a(n) = lod_4(A000045(n)).
From Philippe Deléham, Nov 30 2023: (Start)
a(n) = 2*a(n-6) - a(n-12) for n >= 12.
a(6*n) = 4*n, a(6*n+1) = 12*n+1, a(6*n+2) = 12*n+5, a(6*n+3) = 4*n+2, a(6*n+4) = 4*n+3, a(6*n+5) = 12*n+9.
G.f.: (x + 5*x^2 + 2*x^3 + 3*x^4 + 9*x^5 + 4*x^6 + 11*x^7 + 7*x^8 + 2*x^9 + x^10 + 3*x^11) / ((1-x)^2*(1+x+x^2)^2*(1+x^3)^2). (End)

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

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A079345 Fibonacci(n) mod 16.

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A160080 Lodumo_4 of Fibonacci numbers.

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A287533 Fibonacci numbers modulo 20.

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