Search: id:A079002
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%I A079002
%S A079002 1,2,3,4,5,6,7,9,10,14,15,20,25,27,30,35,45,50,70,75,81,100,125,135,150,
%T A079002 175,225,243,250,350,375,405,500,625,675,729,750,875,1125,1215,1250,
%U A079002 1750,1875,2025,2187,2500,3125,3375,3645,3750,4375,5625,6075,6250,6561
%N A079002 Numbers n such that the Fibonacci residues F(k) mod n form the complete 
               set (0,1,2,....,n-1).
%D A079002 R. L. Graham, D. E. Knuth and O. Patashnick, "Concrete Mathematics", 
               second edition, Addison Wesley, ex. 6.85, p. 318, p. 562
%F A079002 Consists of the integers of the form: 5^k, 2*5^k, 4*5^k, 3^j*5^k, 6*5^k, 
               7*5^k and 14*5^k [see Concrete Mathematics]
%e A079002 Fibonacci numbers (A000045) are 0,1,1,2,3,5,8,.. and mod 5 these are 
               0,1,1,2,3,0,3,3,4,... i.e. all possible remainders mod 5 occur in 
               the Fib series mod 5, so 5 is in the series. This is not true for 
               n=8 so 8 is not in the series.
%Y A079002 Cf. A066853, A001175.
%Y A079002 Sequence in context: A087950 A060527 A152493 this_sequence A119984 A059879 
               A049537
%Y A079002 Adjacent sequences: A078999 A079000 A079001 this_sequence A079003 A079004 
               A079005
%K A079002 nonn
%O A079002 1,2
%A A079002 Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 01 2003
%E A079002 Corrected by Ron Knott (ron(AT)ronknott.com), Jan 05 2005
%E A079002 Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Nov 28 2006, 
               following a suggestion from Martin Fuller (martin_n_fuller(AT)btinternet.com)

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