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

%I A123976 #15 Jul 17 2025 21:45:11
%S A123976 1,11,19,29,31,41,59,61,71,79,89,101,109,131,139,149,151,179,181,191,
%T A123976 199,211,229,239,241,251,269,271,281,311,331,349,359,379,389,401,409,
%U A123976 419,421,431,439,442,449,461,479,491,499,509,521,541,569,571,599,601
%N A123976 Numbers k such that Fibonacci(k-1) is divisible by k.
%C A123976 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
%H A123976 Reinhard Zumkeller, <a href="/A123976/b123976.txt">Table of n, a(n) for n = 1..1000</a>
%e A123976 Fibonacci(10) = 55, is divisible by 11.
%t A123976 Select[Range[1000], IntegerQ[Fibonacci[ # - 1]/# ] &]
%o A123976 (Haskell)
%o A123976 import Data.List (elemIndices)
%o A123976 a123976 n = a123976_list !! (n-1)
%o A123976 a123976_list = map (+ 1) $ elemIndices 0 $ zipWith mod a000045_list [1..]
%o A123976 -- _Reinhard Zumkeller_, Oct 13 2011
%o A123976 (PARI) is(n)=((Mod([1,1;1,0],n))^n)[2,2]==0 \\ _Charles R Greathouse IV_, Feb 03 2014
%Y A123976 Cf. A069106, A045468, A069104, A069107, A003631, A000045, A023172, A159051.
%K A123976 nonn
%O A123976 1,2
%A A123976 _Tanya Khovanova_, Oct 30 2006