Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
A123976
Numbers n such that Fibonacci(n-1) is divisible by n.
10
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
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
KEYWORD
nonn
AUTHOR
Tanya Khovanova, Oct 30 2006
STATUS
approved