login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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.

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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 19 16:32 EST 2019. Contains 319309 sequences. (Running on oeis4.)