A253246 - OEIS

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A253246

Pisano period of A006190 to mod prime(n).

3, 2, 12, 16, 8, 52, 16, 40, 22, 28, 64, 76, 28, 42, 96, 26, 24, 30, 136, 144, 148, 26, 168, 180, 196, 50, 102, 106, 20, 112, 126, 10, 92, 138, 300, 304, 156, 328, 336, 86, 178, 180, 190, 388, 396, 198, 30, 448, 456, 460, 116, 160, 484, 250, 128, 262, 268, 544, 138, 564

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OFFSET

1,1

COMMENTS

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).

In fact, the conjecture fails on p=241, and this is the only counterexample below 10^8.

LINKS

Eric Chen, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = A175182(A000040(n)).

MATHEMATICA

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}]

PROG

(PARI)

fibmod(n, m)=((Mod([3, 1; 1, 0], m))^n)[1, 2]

entry(p)=my(k=1, c=Mod(1, p), o); while(c, [o, c]=[c, 3*c+o]; k++); ka(n)=entry(prime(n))

CROSSREFS