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A253246 Pisano period of A006190 to mod prime(n).

%I A253246 #11 Apr 19 2015 20:39:28
%S A253246 3,2,12,16,8,52,16,40,22,28,64,76,28,42,96,26,24,30,136,144,148,26,
%T A253246 168,180,196,50,102,106,20,112,126,10,92,138,300,304,156,328,336,86,
%U A253246 178,180,190,388,396,198,30,448,456,460,116,160,484,250,128,262,268,544,138,564
%N A253246 Pisano period of A006190 to mod prime(n).
%C A253246 If the generalized Wall's conjecture to A006190 is true, then we can calculate A175182(m) when m is a prime power since for any k>=1 : A175182(prime(n)^k)=a(n)*prime(n)^(k-1). For example: A175182(2^k)=3*2^(k-1)=A007283(k-1).
%C A253246 In fact, the conjecture fails on p=241, and this is the only counterexample below 10^8.
%H A253246 Eric Chen, <a href="/A253246/b253246.txt">Table of n, a(n) for n = 1..1000</a>
%F A253246 a(n) = A175182(A000040(n)).
%t A253246 Table[s = t = Mod[{0, 1}, Prime[n]]; cnt = 1; While[tmp = Mod[3*t[[2]] + t[[1]], n]; t[[1]] = t[[2]]; t[[2]] = tmp; s!= t, cnt++]; cnt, {n, 100}]
%o A253246 (PARI)
%o A253246 fibmod(n, m)=((Mod([3, 1; 1, 0], m))^n)[1, 2]
%o A253246 entry(p)=my(k=1, c=Mod(1, p), o); while(c, [o, c]=[c, 3*c+o]; k++); ka(n)=entry(prime(n))
%Y A253246 Cf. A060305, A175182.
%K A253246 nonn
%O A253246 1,1
%A A253246 _Eric Chen_, Apr 11 2015