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

2, 3, 7, 43, 79, 547, 3319, 6163, 36979, 42667, 258847, 1553119, 1573207, 1834639, 1854763, 11131927, 20224159, 20451679, 124027567, 141569107, 141588763, 467477683, 1840398379, 3278780359, 5276533183, 6089163523, 6155955079, 11168428363, 11185512199, 31655671459

Offset

1,1

Comments

Is this sequence infinite?

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

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[100000]], is[#, 13] &]

Prog

(PARI)
leastdiv(v, pred, inf)={ \\ finds least divisor d satisfying pred(d) && d>=inf
  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))));
  my(stop=vecprod(v), lim=inf, m=4);
  while(lim<=stop, lim*=m; my(d=recurse(0, 1, lim)); if(d<lim, return(d), m*=4*sqrtint(m))); oo;
}
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

Crossrefs

Cf. A267503, A267504, A267506, A267507, A005117, A227455, A227007, A227006.

Sequence in context: A282027 A255595 A085682 * A267506 A218467 A241166

Adjacent sequences: A267502 A267503 A267504 * A267506 A267507 A267508

Keyword

nonn

Author

José María Grau Ribas, Jan 16 2016

Extensions

Terms a(16) and beyond from Andrew Howroyd, Nov 13 2018

Status

approved