OFFSET
1,8
COMMENTS
If n belongs to A079002, then a(n) = 0. - Michel Marcus, May 27 2013
a(n) = number of zeros in n-th row of triangle A128924. - Reinhard Zumkeller, Jan 16 2014
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Cyrus Hsia et al., Mathematical Mayhem Editors, Fibonacci residues, Crux Mathematicorum, 1997 Vol. 23 No. 4, pp. 224-226.
Casey Mongoven, Sonification of multiple Fibonacci-related sequences, Annales Mathematicae et Informaticae, 41 (2013) pp. 175-192.
D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly (67 #6, Jun-Jul 1960), pp. 525-532.
FORMULA
a(n) = n - A066853(n). - Michel Marcus, May 27 2013
EXAMPLE
The Fibonacci sequence mod 8 is { 0 1 1 2 3 5 0 5 5 2 7 1 0 1 1 ... } - a periodic sequence with a period of 12 (see A001175). Two residues do not occur in this sequence (4 and 6), therefore a(8) = 2.
MATHEMATICA
With[{fibs=Fibonacci[Range[300]]}, Table[Length[Complement[Range[0, n-1], Union[ Mod[fibs, n]]]], {n, 80}]] (* Harvey P. Dale, Jul 01 2021 *)
PROG
(Haskell)
a118965 = sum . map (0 ^) . a128924_row
-- Reinhard Zumkeller, Jan 16 2014
(PARI) a(n)=if(n<8, return(0)); my(v=List([1, 2])); while(v[#v] || v[#v-1]!=1, listput(v, (v[#v]+v[#v-1])%n)); n-#Set(v) \\ Charles R Greathouse IV, Jun 20 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Casey Mongoven, May 07 2006
EXTENSIONS
Offset corrected by Michel Marcus, May 27 2013
STATUS
approved