A267503 Primes p such that p-1 is squarefree and all prime divisors of p-1 other than 5 are also in the sequence.

2, 3, 7, 11, 23, 31, 43, 47, 67, 71, 139, 211, 283, 311, 331, 431, 463, 659, 683, 691, 863, 947, 967, 1291, 1303, 1319, 1367, 1427, 1699, 1867, 1979, 1987, 2011, 2111, 2131, 2311, 2531, 3011, 3083, 4099, 4423, 4643, 4691, 4831, 5171, 5179, 5683, 5839, 6299, 6911, 7283, 7591, 8563, 8863, 9227, 9871, 9931, 10343, 10627, 11887, 11923, 12911

Offset: 1

Author

José María Grau Ribas, Jan 16 2016

Keywords

• nonn

Comments

Is this sequence infinite?

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A267504, A267505, A267506, A267507, A005117, A227455, A227007, A227006.

Programs

Maple

N:= 20000: # to get all terms <= N
Res:= 2:
Agenda:= {3,11}:
P:= {2,10}:
g:= proc(t) local s; s:=  p*t; if s < N then s else NULL fi end proc:
while Agenda <> {} do
  p:= min(Agenda);
  Res:= Res, p;
  newP:= map(g , P);
  P:= P union newP;
  Agenda:= Agenda minus {p} union select(isprime, map(`+`,newP,1));
od:
Res; # Robert Israel, Mar 15 2019

Mathematica

fa = FactorInteger; is[2, p_] = True; is[2, p_];
is[n_, p_] := PrimeQ[n] &&  MoebiusMu[n - 1] ≠ 0 && Union@Table[is[fa[n - 1][[i, 1]], p] || fa[n - 1][[ i, 1]] == p , {i, Length[fa[n - 1]]}] == {True}; Select[Prime[Range[10000]], is[#, 5] &]