|
|
A118965
|
|
Number of missing residues in Fibonacci sequence mod n.
|
|
4
|
|
|
0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 1, 4, 0, 0, 5, 4, 7, 7, 0, 12, 8, 4, 11, 0, 8, 0, 7, 19, 0, 12, 11, 14, 21, 0, 21, 8, 25, 14, 10, 22, 24, 10, 24, 0, 25, 32, 33, 12, 0, 16, 22, 16, 25, 43, 31, 24, 38, 22, 5, 36, 41, 40, 22, 20, 28, 16, 48, 40, 0, 27, 57
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,8
|
|
COMMENTS
|
|
|
LINKS
|
Cyrus Hsia et al., Mathematical Mayhem Editors, Fibonacci residues, Crux Mathematicorum, 1997 Vol. 23 No. 4, pp. 224-226.
|
|
FORMULA
|
|
|
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
(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
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|