A284786 Pisano period of sequence A006054 modulo n.

1, 7, 26, 14, 62, 182, 42, 28, 78, 434, 266, 182, 12, 42, 806, 56, 614, 546, 254, 434, 546, 266, 1106, 364, 310, 84, 234, 42, 28, 5642, 1986, 112, 3458, 4298, 1302, 546, 2814, 1778, 156, 868, 40, 546, 42, 266, 2418, 1106, 4514, 728, 294, 2170, 7982, 84, 5726, 1638, 8246, 84, 3302, 28, 7082, 5642, 582

Offset

1,2

Links

Table of n, a(n) for n=1..61.

Robert Israel, Mathematics StackExchange, When does x^3-x^2-2x+1 split mod p.

Wikipedia, Pisano period.

Formula

From Robert Israel, Jun 14 2017: (Start)

If m and n are coprime, a(m*n) = lcm(a(m),a(n)).

If p is a prime such that the polynomial x^3-x^2-2*x+1 splits into distinct factors mod p, then a(p) divides p-1. These primes are A045472. (End)

Maple

f:= proc(n) option remember; local F, t, k, a;
F:= ifactors(n)[2];
if nops(F) > 1 then
  return(ilcm(seq(procname(t[1]^t[2]), t=F)))
fi;
a:= [0, 0, 1];
for k from 1 do
  a:= [a[2], a[3], 2*a[3]+a[2]-a[1] mod n];
  if  a = [0, 0, 1] then return k fi;
od:
end proc:
f(1):= 1:
map(f, [$1..100]); # Robert Israel, Jun 14 2017

Mathematica

Table[FindTransientRepeat[
    Mod[LinearRecurrence[{2, 1, -1}, {0, 0, 1}, 100000], n], 2] //
   Last // Length, {n, 1, 20}]

Crossrefs

Cf. A001175 Pisano periods of Fibonacci numbers mod n.

Cf. A045472.

Sequence in context: A373162 A063453 A284054 * A262109 A276614 A230399

Adjacent sequences: A284783 A284784 A284785 * A284787 A284788 A284789

Keyword

nonn

Author

Patrick D McLean, Apr 02 2017

Extensions

More terms from Robert Israel, Jun 14 2017

Status

approved