OFFSET
1,1
COMMENTS
The first term not in A371566 is a(105) = 4259.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Fibonacci n-Step Number
Robert Israel, Linear Recurrences With a Single Minimal Period
EXAMPLE
a(3) = 11 is a term because the recurrence has period 16105 for all initial conditions except (0,0,0,0,0).
MAPLE
filter:= proc(p) local Q, q, F, i, z, d, k, kp, G, alpha;
Q:= z^5 - z^4 - z^3 - z^2 - z - 1;
if Irreduc(Q) mod p then return true fi;
F:= (Factors(Q) mod p)[2];
if ormap(t -> t[2]>1, F) then return false fi;
for i from 1 to nops(F) do
q:= F[i][1];
d:= degree(q);
if d = 1 then
kp:= numtheory:-order(solve(q, z), p);
else
G:= GF(p, d, q);
alpha:= G:-ConvertIn(z);
kp:= G:-order(alpha);
fi;
if i = 1 then k:= kp
elif kp <> k then return false
fi;
od;
true
end proc:
select(filter, [seq(ithprime(i), i=1..1000)]);
CROSSREFS
KEYWORD
nonn,more
AUTHOR
T. D. Noe, May 02 2005, revised May 12 2005
EXTENSIONS
4259 found by D. S. McNeil.
Edited by Robert Israel, Mar 27 2024
STATUS
approved