login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A218358 Minimal order of degree-n irreducible polynomials over GF(7). 8
1, 4, 9, 5, 2801, 36, 29, 64, 27, 11, 1123, 13, 16148168401, 113, 31, 17, 14009, 108, 419, 55, 261, 23, 47, 73, 2551, 53, 81, 145, 59, 99, 311, 256, 3631, 56036, 81229, 135, 223, 1676, 486643, 41, 83, 1017, 166003607842448777, 115, 837, 188, 13722816749522711 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(n) < 7^n.
LINKS
Eric Weisstein's World of Mathematics, Irreducible Polynomial
Eric Weisstein's World of Mathematics, Polynomial Order
FORMULA
a(n) = min(M(n)) with M(n) = {d : d|(7^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}.
a(n) = A212486(n,1) = A213224(n,4).
MAPLE
with(numtheory):
M:= proc(n) M(n):= divisors(7^n-1) minus U(n-1) end:
U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:
a:= n-> min(M(n)[]):
seq(a(n), n=1..42);
MATHEMATICA
M[n_] := M[n] = Divisors[7^n - 1]~Complement~U[n - 1];
U[n_] := U[n] = If[n == 0, {}, M[n]~Union~U[n - 1]];
a[n_] := Min[M[n]];
Table[a[n], {n, 1, 47}] (* Jean-François Alcover, Oct 24 2022, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A163103 A019688 A365725 * A340127 A196403 A238557
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 27 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 02:51 EDT 2024. Contains 370952 sequences. (Running on oeis4.)