

A023162


Numbers k such that F(k) == 1 (mod k), where F(n) = A000045(n) is the nth Fibonacci number.


5



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
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OFFSET

1,2


COMMENTS

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


LINKS



FORMULA

a(n) seems to be asymptotic to c*n*log(n) where c = 1.5...  Benoit Cloitre, Jan 10 2003


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 *)


PROG

(PARI) isok(k) = Mod(fibonacci(k), k) == 1; \\ Michel Marcus, Nov 21 2018


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



