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A267505 Primes p such that p-1 is squarefree and all prime divisors of p-1 other than 13 are also in the sequence.

%I A267505 #22 Feb 16 2021 02:10:05
%S A267505 2,3,7,43,79,547,3319,6163,36979,42667,258847,1553119,1573207,1834639,
%T A267505 1854763,11131927,20224159,20451679,124027567,141569107,141588763,
%U A267505 467477683,1840398379,3278780359,5276533183,6089163523,6155955079,11168428363,11185512199,31655671459
%N A267505 Primes p such that p-1 is squarefree and all prime divisors of p-1 other than 13 are also in the sequence.
%C A267505 Is this sequence infinite?
%H A267505 Andrew Howroyd, <a href="/A267505/b267505.txt">Table of n, a(n) for n = 1..500</a>
%t A267505 fa = FactorInteger; is[2, p_] = True; is[2, p_];
%t A267505 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[100000]], is[#, 13] &]
%o A267505 (PARI)
%o A267505 leastdiv(v, pred, inf)={ \\ finds least divisor d satisfying pred(d) && d>=inf
%o A267505   my(recurse(k,d,lim)= if(d >= lim, lim, if(d>=inf && pred(d), d, k++; if(k<=#v, lim=self()(k, d*v[k], lim); self()(k, d, lim), lim))));
%o A267505   my(stop=vecprod(v), lim=inf, m=4);
%o A267505   while(lim<=stop, lim*=m; my(d=recurse(0,1,lim)); if(d<lim, return(d), m*=4*sqrtint(m))); oo;
%o A267505 }
%o A267505 lista(n, S=[13])={my(t=2); print1(t, ", "); for(i=2, n, S=concat(S, [t]); t=leastdiv(S, d->isprime(d+1), S[#S]); if(t==oo, break); t++; print1(t, ", "))} \\ _Andrew Howroyd_, Nov 13 2018
%Y A267505 Cf. A267503, A267504, A267506, A267507, A005117, A227455, A227007, A227006.
%K A267505 nonn
%O A267505 1,1
%A A267505 _José María Grau Ribas_, Jan 16 2016
%E A267505 Terms a(16) and beyond from _Andrew Howroyd_, Nov 13 2018