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

Author

Reinhard Zumkeller, Oct 08 2003

Keywords

• nonn
• more

Comments

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

Crossrefs

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

Programs

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 *)

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

Formula

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

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