A279071 Numbers k such that Fibonacci(k) == +-1 (mod k).

1, 2, 3, 4, 7, 11, 13, 14, 17, 19, 22, 23, 26, 29, 31, 34, 37, 38, 41, 43, 46, 47, 53, 58, 59, 61, 62, 67, 71, 73, 74, 79, 82, 83, 86, 89, 94, 97, 101, 103, 106, 107, 109, 113, 118, 122, 127, 131, 134, 137, 139, 142, 146, 149, 151, 157, 158, 163, 166, 167, 173

Offset

1,2

Comments

The terms of this sequence are 1, every prime except 5, every "twice prime" except 6 and 10, and the terms of A279072, i.e., {323, 572, 646, 754, 2737, 3782, 4181, 5474, 5777, 6479, ...}.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

1 is in the sequence because Fibonacci(1) mod 1 = 1 mod 1 = 0 and +-1 mod 1 = 0.
2 is in the sequence because Fibonacci(2) mod 2 = 1 mod 2 = 1.
3 is in the sequence because Fibonacci(3) mod 3 = 2 mod 3 = 2 and -1 mod 3 = 2.

Mathematica

Select[Range[200], MemberQ[{1, # - 1}, Mod[Fibonacci[#], #]] &] (* Amiram Eldar, Jun 13 2020 *)

Crossrefs

Cf. A000045, A279072.

Sequence in context: A102282 A353178 A232543 * A171027 A348792 A064933

Adjacent sequences: A279068 A279069 A279070 * A279072 A279073 A279074

Keyword

nonn

Author

Jon E. Schoenfield, Dec 30 2016

Status

approved