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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.
5
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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(16) and beyond from Andrew Howroyd, Nov 13 2018
STATUS
approved