A088701 - OEIS

%I #23 Aug 18 2018 08:44:38

%S 9,4,10,95,818,2681,16053,35981,797542,1069541,340894,6974465,3586843,

%T 2070050198,5238280946,14499777101,2601693504238,7472089131123

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

%C Is this sequence infinite? - _David A. Corneth_, Aug 17 2018

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

%t 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 *)

%o (Perl) use ntheory ":all";

%o my($l,$nextn,@C)=(4,0);

%o forcomposites {

%o   if (is_semiprime($_)) {

%o     my $c = prime_count($l+1,$_-1);

%o     if (!defined $C[$c]) {

%o       $C[$c] = $l;

%o       while (defined $C[$nextn]) { print "$nextn $C[$nextn]\n"; $nextn++; }

%o     }

%o     $l = $_;

%o   }

%o } 5,1e7;  # _Dana Jacobsen_, Aug 16 2018

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

%K nonn,more

%O 0,1

%A _Reinhard Zumkeller_, Oct 08 2003

%E a(11)-a(15) from _Donovan Johnson_, Mar 14 2010

%E a(16) from _Giovanni Resta_, Aug 17 2018

%E a(17) from _Giovanni Resta_, Aug 18 2018