A111419 a(n) is the smallest positive integer for which Fibonacci(n + a(n)) == Fibonacci(n) (mod n).

1, 2, 2, 6, 5, 15, 2, 9, 6, 10, 1, 12, 2, 9, 10, 24, 2, 24, 1, 5, 6, 7, 2, 12, 25, 15, 18, 48, 1, 15, 1, 11, 14, 19, 10, 12, 2, 15, 34, 60, 1, 15, 2, 30, 30, 25, 2, 12, 14, 50, 42, 78, 2, 24, 10, 24, 30, 13, 1, 60, 1, 27, 18, 96, 10, 120, 2, 36, 6, 25, 1, 12, 2, 39, 50, 18, 6, 39, 1, 35

Offset

1,2

Comments

When a(n)=2, n is often prime. The exceptions (323, 377, 2834, ...) are in A069107.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

a(3) = 2 because Fibonacci(3+2) - Fibonacci(3) = 5 - 2 == 0 (mod 3) and 2 is the smallest integer for which this is true.

Mathematica

Array[Block[{k = 1}, While[Mod[Fibonacci[# + k], #] != Mod[Fibonacci@ #, #], k++]; k] &, 80] (* Michael De Vlieger, Dec 17 2017 *)

Prog

(MuPAD) for n from 1 to 100 do an := 0; repeat an := an+1; until (numlib::fibonacci(n+an)-numlib::fibonacci(n)) mod n = 0 end_repeat; print(an); end_for;
(PARI) a(n) = {my(k = 1); while(Mod(fibonacci(n + k), n) != Mod(fibonacci(n), n), k++); k; } \\ Michel Marcus, Dec 18 2017

Crossrefs

Cf. A002708.

Sequence in context: A156563 A201500 A054917 * A360087 A306768 A174399

Adjacent sequences: A111416 A111417 A111418 * A111420 A111421 A111422

Keyword

nonn

Author

Stefan Steinerberger, Nov 13 2005

Status

approved