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 A218356 Minimal order of degree-n irreducible polynomials over GF(3). 7
 1, 4, 13, 5, 11, 7, 1093, 32, 757, 44, 23, 35, 797161, 547, 143, 17, 1871, 19, 1597, 25, 14209, 67, 47, 224, 8951, 398581, 109, 29, 59, 31, 683, 128, 299, 103, 71, 95, 13097927, 2851, 169, 352, 83, 43, 431, 115, 181, 188, 1223, 97, 491, 151, 12853, 53, 107 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) < 3^n. For n > 2, a(n) <= A143663(n). For odd prime n, a(n) = A143663(n). - Max Alekseyev, Apr 30 2022 LINKS Max Alekseyev, Table of n, a(n) for n = 1..796 (first 100 terms from Alois P. Heinz) FORMULA a(n) = min(M(n)) with M(n) = {d : d|(3^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}. a(n) = A212906(n,1) = A213224(n,2). MAPLE M:= proc(n) M(n):= numtheory[divisors](3^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..60); MATHEMATICA M[n_] := M[n] = Divisors[3^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, 60}] (* Jean-François Alcover, Oct 24 2022, after Alois P. Heinz *) CROSSREFS Cf. A143663, A212906, A213224, A235366. Sequence in context: A170865 A320030 A191509 * A249120 A170844 A051432 Adjacent sequences: A218353 A218354 A218355 * A218357 A218358 A218359 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 27 2012 STATUS approved

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Last modified February 26 02:19 EST 2024. Contains 370335 sequences. (Running on oeis4.)