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 A218357 Minimal order of degree-n irreducible polynomials over GF(5). 6
 1, 3, 31, 13, 11, 7, 19531, 32, 19, 33, 12207031, 91, 305175781, 29, 181, 17, 409, 27, 191, 41, 379, 23, 8971, 224, 101, 5227, 109, 377, 59, 61, 1861, 128, 199, 1227, 211, 37, 149, 573, 79, 241, 2238236249, 43, 1644512641, 89, 209, 47, 177635683940025046467781066894531 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) < 5^n. a(n) <= A143665(n). For prime n, a(n) = A143665(n). - Max Alekseyev, Apr 30 2022 LINKS Max Alekseyev, Table of n, a(n) for n = 1..520 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|(5^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}. a(n) = A212485(n,1) = A213224(n,3). MAPLE with(numtheory): M:= proc(n) M(n):= divisors(5^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..47); MATHEMATICA M[n_] := M[n] = Divisors[5^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, Mar 24 2017, translated from Maple *) CROSSREFS Cf. A212485, A213224. Sequence in context: A322777 A089281 A212729 * A090543 A215946 A139090 Adjacent sequences: A218354 A218355 A218356 * A218358 A218359 A218360 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 27 2012 STATUS approved

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Last modified January 29 00:02 EST 2023. Contains 359905 sequences. (Running on oeis4.)