

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
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OFFSET

1,8


COMMENTS

If n belongs to A079002, then a(n) = 0.  Michel Marcus, May 27 2013
a(n) = number of zeros in nth 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. 224226.
Casey Mongoven, Sonification of multiple Fibonaccirelated sequences, Annales Mathematicae et Informaticae, 41 (2013) pp. 175192.
D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly (67 #6, JunJul 1960), pp. 525532.


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.


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[#v1]!=1, listput(v, (v[#v]+v[#v1])%n)); n#Set(v) \\ Charles R Greathouse IV, Jun 20 2017


CROSSREFS

Cf. A066853, A001175.
Sequence in context: A238858 A106235 A288098 * A252729 A121552 A158118
Adjacent sequences: A118962 A118963 A118964 * A118966 A118967 A118968


KEYWORD

nonn


AUTHOR

Casey Mongoven, May 07 2006


EXTENSIONS

Offset corrected by Michel Marcus, May 27 2013


STATUS

approved



