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A023162 Numbers k such that F(k) == -1 (mod k), where F(n) = A000045(n) is the n-th 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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A207573 A152605 A285222 * A022437 A057983 A200088
KEYWORD
nonn
AUTHOR
EXTENSIONS
Name clarified by Alonso del Arte and Michel Marcus, Nov 20 2018
STATUS
approved

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Last modified May 24 23:50 EDT 2024. Contains 372782 sequences. (Running on oeis4.)