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

%I A267503 #26 Feb 16 2021 02:09:10
%S A267503 2,3,7,11,23,31,43,47,67,71,139,211,283,311,331,431,463,659,683,691,
%T A267503 863,947,967,1291,1303,1319,1367,1427,1699,1867,1979,1987,2011,2111,
%U A267503 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
%N A267503 Primes p such that p-1 is squarefree and all prime divisors of p-1 other than 5 are also in the sequence.
%C A267503 Is this sequence infinite?
%H A267503 Robert Israel, <a href="/A267503/b267503.txt">Table of n, a(n) for n = 1..10000</a>
%p A267503 N:= 20000: # to get all terms <= N
%p A267503 Res:= 2:
%p A267503 Agenda:= {3,11}:
%p A267503 P:= {2,10}:
%p A267503 g:= proc(t) local s; s:=  p*t; if s < N then s else NULL fi end proc:
%p A267503 while Agenda <> {} do
%p A267503   p:= min(Agenda);
%p A267503   Res:= Res, p;
%p A267503   newP:= map(g , P);
%p A267503   P:= P union newP;
%p A267503   Agenda:= Agenda minus {p} union select(isprime, map(`+`,newP,1));
%p A267503 od:
%p A267503 Res; # _Robert Israel_, Mar 15 2019
%t A267503 fa = FactorInteger; is[2, p_] = True; is[2, p_];
%t A267503 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] &]
%Y A267503 Cf. A267504, A267505, A267506, A267507, A005117, A227455, A227007, A227006.
%K A267503 nonn
%O A267503 1,1
%A A267503 _José María Grau Ribas_, Jan 16 2016