login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A218362 Minimal order of degree-n irreducible polynomials over GF(19). 2
1, 4, 27, 16, 151, 7, 701, 17, 81, 11, 104281, 13, 599, 197, 31, 64, 3044803, 199, 109912203092239643840221, 176, 18927, 23, 277, 119, 101, 131, 243, 29, 59, 61, 243270318891483838103593381595151809701, 97, 67, 12179212, 71, 37, 149, 108301, 79, 41, 10654507 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) < 19^n.

LINKS

Table of n, a(n) for n=1..41.

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|(19^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}.

a(n) = A218339(n,1) = A213224(n,8).

MAPLE

with(numtheory):

M:= proc(n) M(n):= divisors(19^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..28);

CROSSREFS

Cf. A213224, A218339.

Sequence in context: A125723 A094543 A136511 * A108138 A119361 A133482

Adjacent sequences:  A218359 A218360 A218361 * A218363 A218364 A218365

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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 27 22:50 EST 2020. Contains 332319 sequences. (Running on oeis4.)