A206945 - OEIS

%I #28 May 10 2021 02:07:37

%S 3,7,11,13,31,43,61,73,127,151,157,211,241,307,331,421,463,521,547,

%T 601,683,757,1093,1123,1483,1723,2551,2731,2801,2971,3307,3541,3907,

%U 4423,4561,4831,5113,5419,5701,6007,6163,6481,8011,8191,9091,9901,10303,11131

%N Prime numbers Phi(k,m) with integer k > 2, |m| > 1, and k != 2^j (j > 1)

%C Phi(k,m) denotes the cyclotomic polynomial numbers Cyclotomic(k,m).

%C These are the prime terms of A206944.

%C A059055 is a subsequence of this sequence.

%C The Mathematica program can generate this sequence to arbitrary boundary maxdata without a user's choice of parameters. The parameter determination part of this program is explained at A206864.

%e Just taking prime terms from A206944:

%e A206944(1)=3 is prime, so a(1)=3 ...

%t phiinv[n_, pl_] := Module[{i, p, e, pe, val}, If[pl == {}, Return[If[n == 1, {1}, {}]]]; val = {}; p = Last[pl]; For[e = 0; pe = 1, e == 0 || Mod[n, (p - 1) pe/p] == 0, e++; pe *= p, val = Join[val, pe*phiinv[If[e == 0, n, n*p/pe/(p - 1)], Drop[pl, -1]]]]; Sort[val]]; phiinv[n_] := phiinv[n, Select[1 + Divisors[n], PrimeQ]]; maxdata = 12000; max = Ceiling[(1 + Sqrt[1 + 4*(maxdata - 1)])/4]*2; eb = 2*Floor[(Log[2, maxdata])/2 + 0.5]; While[eg = phiinv[eb]; lu = Length[eg]; lu == 0, eb = eb + 2]; t = Select[Range[eg[[Length[eg]]]], ((EulerPhi[#] <= eb) && ((! IntegerQ[Log[2, #]]) || (# <= 2))) &]; t = SortBy[t, Cyclotomic[#, 2] &]; a = {}; Do[i = 2; While[i++; cc = Cyclotomic[t[[i]], m]; cc <= maxdata, If[PrimeQ[cc], a = Append[a, cc]]], {m, 2, max}]; Union[a]

%Y Cf. A059055, A206944, A206942, A206864, A194712.

%K nonn

%O 1,1

%A _Lei Zhou_, Feb 13 2012