A206945 Prime numbers Phi(k,m) with integer k > 2, |m| > 1, and k != 2^j (j > 1)

3, 7, 11, 13, 31, 43, 61, 73, 127, 151, 157, 211, 241, 307, 331, 421, 463, 521, 547, 601, 683, 757, 1093, 1123, 1483, 1723, 2551, 2731, 2801, 2971, 3307, 3541, 3907, 4423, 4561, 4831, 5113, 5419, 5701, 6007, 6163, 6481, 8011, 8191, 9091, 9901, 10303, 11131

Offset

1,1

Comments

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

These are the prime terms of A206944.

A059055 is a subsequence of this sequence.

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.

Links

Table of n, a(n) for n=1..48.

Example

Just taking prime terms from A206944:
A206944(1)=3 is prime, so a(1)=3 ...

Mathematica

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]

Crossrefs

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

Sequence in context: A164568 A053728 A342183 * A206946 A059055 A243367

Adjacent sequences: A206942 A206943 A206944 * A206946 A206947 A206948

Keyword

nonn

Author

Lei Zhou, Feb 13 2012

Status

approved