Search: id:A001176
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%I A001176 M0165 N0064
%S A001176 1,1,2,1,4,2,2,2,2,4,1,2,4,2,2,2,4,2,1,2,2,1,2,2,4,4,2,2,1,2,1,2,2,4,2,
%T A001176 2,4,1,2,2,2,2,2,1,2,2,2,2,2,4,2,2,4,2,2,2,2,1,1,2,4,1,2,2,4,2,2,2,2,2,
%U A001176 1,2,4,4,2,1,2,2,1,2,2,2,2,2,4,2,2,2,4,2,2,2,2,2,2,2,4,2,2,2,1,2,2,2,2
%N A001176 Number of zeros in fundamental period of Fibonacci numbers mod n.
%C A001176 If the Fibonacci numbers are indexed so that 3 is the fourth number, 
               then if the modulo base is a Fibonacci number (>= 3) with an even 
               index, the period has 2 zeros. If the base is a Fibonacci number 
               (>= 5) with an odd index, the period has 4 zeros. - Kerry Mitchell 
               (lkmitch(AT)gmail.com), Dec 11 2005
%D A001176 J. D. Fulton and W. L. Morris, On arithmetical functions related to the 
               Fibonacci numbers, Acta Arithmetica, 16 (1969), 105-110.
%D A001176 B. H. Hannon and W. L. Morris, Tables of Arithmetical Functions Related 
               to the Fibonacci Numbers. Report ORNL-4261, Oak Ridge National Laboratory, 
               Oak Ridge, Tennessee, Jun 1968.
%D A001176 Review of B. H. Hannon and W. L. Morris tables, Math. Comp., 23 (1969), 
               459-460.
%D A001176 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001176 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A001176 T. D. Noe, <a href="b001176.txt">Table of n, a(n) for n=1..1000</a>
%H A001176 M. Renault, <a href="http://www.math.temple.edu/~renault/fibonacci/fiblist.html">
               Fibonacci sequence modulo m</a>
%F A001176 a(n) = A001175(n)/A001177(n) for n >= 1.
%e A001176 {F(n) mod 1} has fundamental period (0) with 1 zero.
%e A001176 {F(n) mod 2} has fundamental period (0,1,1) with 1 zero.
%e A001176 {F(n) mod 3} has fundamental period (0,1,1,2,0,2,2,1) with 2 zeros.
%e A001176 {F(n) mod 4} has fundamental period (0,1,1,2,3,1), with 1 zero.
%e A001176 {F(n) mod 5} has fundamental period (0,1,1,2,3,0,3,3,1,4,0,4,4,3,2,0,
               2,2,4,1) with 4 zeros.
%Y A001176 Cf. A001175, A001177, A053027, A053028, A053029, A053030, A053031, A053032.
%Y A001176 Sequence in context: A109090 A080100 A161822 this_sequence A136693 A086685 
               A094571
%Y A001176 Adjacent sequences: A001173 A001174 A001175 this_sequence A001177 A001178 
               A001179
%K A001176 nonn,easy
%O A001176 1,3
%A A001176 N. J. A. Sloane (njas(AT)research.att.com).
%E A001176 Better description and more terms from Henry Bottomley (se16(AT)btinternet.com), 
               Feb 01 2000. Examples from David W. Wilson, Jan 05 2005.

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