A137750 Number of distinct residues in the Fibonacci sequence mod the n-th prime.

2, 3, 5, 7, 7, 9, 13, 12, 19, 10, 19, 29, 19, 33, 15, 37, 37, 25, 51, 44, 57, 49, 63, 17, 69, 35, 79, 33, 49, 33, 97, 82, 109, 33, 61, 37, 113, 123, 127, 137, 112, 62, 119, 149, 149, 16, 30, 169, 171, 80, 21, 149, 103, 157, 193, 85

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Casey Mongoven, Unique Residues Primes no. 1; electro-acoustic music created with this sequence.

Formula

a(n) = A066853(A000040(n)). - Max Alekseyev, Feb 08 2023

Example

The 5th prime number is 11. The Fibonacci sequence mod 11 is {0,1,1,2,3,5,8,2,10,1,0,1,...} - a periodic sequence. There are 7 distinct residues in this sequence, namely {0,1,2,3,5,8,10}. So a(5) = 7.

Mathematica

With[{f=Fibonacci[Range[500]]}, Table[Length[Union[Mod[f, Prime[n]]]], {n, 60}]] (* Harvey P. Dale, Aug 15 2012 *)

Prog

(PARI) a(n)=my(v=List([0, 1]), p=prime(n)); while(v[#v]||v[#v-1]!=1, listput(v, (v[#v]+v[#v-1])%p)); #vecsort(Vec(v), , 8) \\ Charles R Greathouse IV, Apr 24 2012

Crossrefs

Cf. A066853, A137751, A000045, A001175.

Sequence in context: A296375 A306923 A366856 * A196365 A195882 A332333

Adjacent sequences: A137747 A137748 A137749 * A137751 A137752 A137753

Keyword

nonn

Author

Casey Mongoven, Feb 10 2008

Status

approved