A088701 Smallest semiprime such that n primes will follow until the next semiprime.

9, 4, 10, 95, 818, 2681, 16053, 35981, 797542, 1069541, 340894, 6974465, 3586843, 2070050198, 5238280946, 14499777101, 2601693504238, 7472089131123

Offset

0,1

Comments

Is this sequence infinite? - David A. Corneth, Aug 17 2018

Links

Table of n, a(n) for n=0..17.

Formula

A088700(a(n)) = n and A088700(k) <> n for 1 <= k < a(n).

Mathematica

om = Array[PrimeOmega, 1100000]; sp = Flatten@ Position[om, 2]; Table[ sp[[ SelectFirst[ Range[Length[sp] - 1], Count[Take[om, {sp[[#]], sp[[# + 1]]}], x_ /; x == 1] == j &, 0]]], {j, 0, 10}] (* Giovanni Resta, Aug 16 2018 *)

Prog

(Perl) use ntheory ":all";
my($l, $nextn, @C)=(4, 0);
forcomposites {
  if (is_semiprime($_)) {
    my $c = prime_count($l+1, $_-1);
    if (!defined $C[$c]) {
      $C[$c] = $l;
      while (defined $C[$nextn]) { print "$nextn $C[$nextn]\n"; $nextn++; }
    }
    $l = $_;
  }
} 5, 1e7;  # Dana Jacobsen, Aug 16 2018

Crossrefs

Cf. A214520 (primes that are the only prime between consecutive semiprimes).

Sequence in context: A253203 A338151 A255642 * A153698 A168203 A248310

Adjacent sequences: A088698 A088699 A088700 * A088702 A088703 A088704

Keyword

nonn,more

Author

Reinhard Zumkeller, Oct 08 2003

Extensions

a(11)-a(15) from Donovan Johnson, Mar 14 2010

a(16) from Giovanni Resta, Aug 17 2018

a(17) from Giovanni Resta, Aug 18 2018

Status

approved