Search: id:A060305
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%I A060305
%S A060305 3,8,20,16,10,28,36,18,48,14,30,76,40,88,32,108,58,60,136,70,148,78,
%T A060305 168,44,196,50,208,72,108,76,256,130,276,46,148,50,316,328,336,348,178,
%U A060305 90,190,388,396,22,42,448,456,114,52,238,240,250,516,176,268,270,556
%N A060305 Related to Pisano periods: period of Fibonacci numbers mod prime(n).
%C A060305 Assuming Wall's conjecture (which is still open) allows one to calculate 
               A001175(m) when m is a prime power since for any k>=1 : A001175(prime(n)^k)=a(n)*prime(n)^(k-1). 
               For example : A001175(2^k)=3*2^(k-1)=A007283(k-1)
%D A060305 D. D. Wall, Fibonacci Series modulo m, American Mathematical Monthly, 
               Vol. 67 - Jun/Jul 1960, pp. 525-532
%H A060305 T. D. Noe, <a href="b060305.txt">Table of n, a(n) for n = 1..1000</a>
%H A060305 A. Elsenhans, J. Jahnel, <a href="http://www.uni-math.gwdg.de/tschinkel/
               gauss/Fibon.pdf">The Fibonacci sequence modulo p^2 -- An investigation 
               by computer for p < 10^14</a>, (2004)
%t A060305 Table[p=Prime[n]; a={1,0}; a0=a; k=0; While[k++; s=Mod[Plus@@a,p];a=RotateLeft[a]; 
               a[[2]]=s; a!=a0]; k, {n,100}] - T. D. Noe (noe(AT)sspectra.com), 
               Jun 12 2006
%o A060305 (PARI) for(n=1,100,s=1; while(sum(i=n,n+s,abs(fibonacci(i)%prime(n)-fibonacci(i+s)%prime(n)))+sum(i=n+1,
               n+1+s,abs(fibonacci(i)%prime(n)-fibonacci(i+s)%prime(n)))>0,s++); 
               print1(s,","))
%Y A060305 Cf. A001175, A000961.
%Y A060305 Cf. A071774, A003147.
%Y A060305 Sequence in context: A086808 A151347 A047093 this_sequence A009141 A090069 
               A027299
%Y A060305 Adjacent sequences: A060302 A060303 A060304 this_sequence A060306 A060307 
               A060308
%K A060305 nonn
%O A060305 1,1
%A A060305 Louis Mello (mellols(AT)aol.com), Mar 26 2001
%E A060305 Corrected by Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 04 2002

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