This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A089911 a(n) = Fibonacci(n) mod 12. 20
 0, 1, 1, 2, 3, 5, 8, 1, 9, 10, 7, 5, 0, 5, 5, 10, 3, 1, 4, 5, 9, 2, 11, 1, 0, 1, 1, 2, 3, 5, 8, 1, 9, 10, 7, 5, 0, 5, 5, 10, 3, 1, 4, 5, 9, 2, 11, 1, 0, 1, 1, 2, 3, 5, 8, 1, 9, 10, 7, 5, 0, 5, 5, 10, 3, 1, 4, 5, 9, 2, 11, 1, 0, 1, 1, 2, 3, 5, 8, 1, 9, 10, 7, 5, 0, 5, 5, 10, 3, 1, 4, 5, 9, 2, 11, 1, 0, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS From Reinhard Zumkeller, Jul 05 2013: (Start) Sequence has been applied by several composers to 12-tone equal temperament pitch structure. The complete Fibonacci mod 12 system (a set of 10 periodic sequences) exhausts all possible ordered dyads; that is, every possible combination of two pitches is found in these sets. a(A008594(n)) = 0; a(A227144(n)) = 1; a(3*A047522(n)) = 2; a(A017569(n)) = a(2*A016933(n)) = a(4*A016777(n)) = 3; a(2*A017629(n)) = a(3*A017137(n)) = a(6*A004767(n)) = 4; a(A227146(n)) = 5; a(nonexistent) = 6; a(2*A017581(n)) = 7; a(2*A017557(n)) = a(4*A016813(n)) = 8; a(A017617(n)) = a(2*A016957(n)) = a(4*A016789(n)) = 9; a(3*A047621(n)) = 10; a(2*A017653(n)) = 11. (End) LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..1199 Ron Knott, Fibonacci Numbers and the Golden Section M. Renault, The Fibonacci Sequence Modulo M A. P. Shah, Fibonacci Sequence Modulo m, Fibonacci Quarterly, Vol.6, No.2 (1968), 139-141. D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly, 67 (1960), 525-532. Index entries for linear recurrences with constant coefficients, signature (1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1). FORMULA Has period of 24, restricted period 12 and multiplier 5. a(n) = (a(n-1) + a(n-2)) mod 12, a(0) = 0, a(1) = 1. MAPLE with(combinat, fibonacci); A089911 := proc(n) fibonacci(n) mod 12; end; MATHEMATICA Table[Mod[Fibonacci[n], 12], {n, 0, 100}] (* Vincenzo Librandi, Feb 04 2014 *) PROG (Haskell) a089911 n = a089911_list !! n a089911_list = 0 : 1 : zipWith (\u v -> (u + v) `mod` 12)                        (tail a089911_list) a089911_list -- Reinhard Zumkeller, Jul 01 2013 (PARI) a(n)=fibonacci(n)%12 \\ Charles R Greathouse IV, Feb 03 2014 (MAGMA) [Fibonacci(n) mod 12: n in [0..100]]; // Vincenzo Librandi, Feb 04 2014 CROSSREFS Cf. A000045, A001175, A003893, A010881. Sequence in context: A093086 A093092 A031111 * A098978 A111301 A247193 Adjacent sequences:  A089908 A089909 A089910 * A089912 A089913 A089914 KEYWORD nonn,hear,easy AUTHOR Casey Mongoven, Nov 14 2003 EXTENSIONS More terms from Ray Chandler, Nov 15 2003 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.

Last modified October 15 22:25 EDT 2019. Contains 328038 sequences. (Running on oeis4.)