A023162 Numbers k such that F(k) == -1 (mod k), where F(n) = A000045(n) is the n-th Fibonacci number.
1, 2, 3, 4, 7, 13, 14, 17, 23, 26, 34, 37, 43, 46, 47, 53, 67, 73, 74, 83, 86, 94, 97, 103, 106, 107, 113, 127, 134, 137, 146, 157, 163, 166, 167, 173, 193, 194, 197, 206, 214, 223, 226, 227, 233, 254, 257, 263, 274, 277, 283, 293, 307, 313, 314, 317, 326, 334
Offset: 1
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
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 *) Select[Range[500], Mod[Fibonacci[#], #] == # - 1 &] (* Alonso del Arte, Nov 20 2018 *) -
PARI
isok(k) = Mod(fibonacci(k), k) == -1; \\ Michel Marcus, Nov 21 2018
Formula
a(n) seems to be asymptotic to c*n*log(n) where c = 1.5... - Benoit Cloitre, Jan 10 2003
Extensions
Name clarified by Alonso del Arte and Michel Marcus, Nov 20 2018
Comments