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A111419 a(n) is the smallest positive integer for which Fibonacci(n + a(n)) == Fibonacci(n) (mod n). 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A174399 A056881 A260322

Adjacent sequences:  A111416 A111417 A111418 * A111420 A111421 A111422

KEYWORD

nonn

AUTHOR

Stefan Steinerberger, Nov 13 2005

STATUS

approved

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Last modified January 19 18:27 EST 2019. Contains 319309 sequences. (Running on oeis4.)