A123976 Numbers n such that Fibonacci(n-1) is divisible by n.

1, 11, 19, 29, 31, 41, 59, 61, 71, 79, 89, 101, 109, 131, 139, 149, 151, 179, 181, 191, 199, 211, 229, 239, 241, 251, 269, 271, 281, 311, 331, 349, 359, 379, 389, 401, 409, 419, 421, 431, 439, 442, 449, 461, 479, 491, 499, 509, 521, 541, 569, 571, 599, 601

Offset

1,2

Comments

a(n) is a union of {1}, A069106(n) and A045468(n). Composite a(n) are listed in A069106(n) = {442, 1891, 2737, 4181, 6601, 6721, 8149, ...}. Prime a(n) are listed in A045468(n) = {11, 19, 29, 31, 41, 59, 61, 71, 79, 89, 101, 109, 131, 139, 149, 151, 179, 181, 191, 199, ...} Primes congruent to {1, 4} mod 5. - Alexander Adamchuk, Nov 02 2006

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Example

Fibonacci(10) = 55, is divisible by 11.

Mathematica

Select[Range[1000], IntegerQ[Fibonacci[ # - 1]/# ] &]

Prog

(Haskell)
import Data.List (elemIndices)
a123976 n = a123976_list !! (n-1)
a123976_list = map (+ 1) $ elemIndices 0 $ zipWith mod a000045_list [1..]
-- Reinhard Zumkeller, Oct 13 2011
(PARI) is(n)=((Mod([1, 1; 1, 0], n))^n)[2, 2]==0 \\ Charles R Greathouse IV, Feb 03 2014

Crossrefs

Cf. A069106, A045468, A069104, A069107, A003631, A000045, A023172, A159051.

Sequence in context: A328896 A057538 A336403 * A045468 A196095 A268271

Adjacent sequences: A123973 A123974 A123975 * A123977 A123978 A123979

Keyword

nonn

Author

Tanya Khovanova, Oct 30 2006

Status

approved