A023162 - OEIS

%I #25 Nov 21 2018 02:31:40

%S 1,2,3,4,7,13,14,17,23,26,34,37,43,46,47,53,67,73,74,83,86,94,97,103,

%T 106,107,113,127,134,137,146,157,163,166,167,173,193,194,197,206,214,

%U 223,226,227,233,254,257,263,274,277,283,293,307,313,314,317,326,334

%N Numbers k such that F(k) == -1 (mod k), where F(n) = A000045(n) is the n-th Fibonacci number.

%C If k is prime then k is in the sequence if and only if k == 2 or 3 (mod 5).

%H Alois P. Heinz, <a href="/A023162/b023162.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) seems to be asymptotic to c*n*log(n) where c = 1.5... - _Benoit Cloitre_, Jan 10 2003

%t Module[{nn = 500, fib}, fib = Thread[{Range[nn], Fibonacci[Range[nn]]}]; Transpose[Select[fib, Mod[Last[#], First[#]] == First[#] - 1 &]][[1]]] (* _Harvey P. Dale_, May 21 2014 *)

%t Select[Range[500], Mod[Fibonacci[#], #] == # - 1 &] (* _Alonso del Arte_, Nov 20 2018 *)

%o (PARI) isok(k) = Mod(fibonacci(k), k) == -1; \\ _Michel Marcus_, Nov 21 2018

%K nonn

%O 1,2

%A _David W. Wilson_

%E Name clarified by _Alonso del Arte_ and _Michel Marcus_, Nov 20 2018