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

Offset: 1

Author

Eric Chen, Apr 11 2015

Keywords

• nonn

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

Crossrefs

Cf. A060305, A175182.

Programs

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}]

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))

Formula

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