A214520 -id:A214520 - cp's OEIS frontend

A088700 Number of primes between successive semiprimes.

1, 1, 0, 2, 0, 2, 0, 1, 0, 2, 0, 0, 1, 0, 2, 1, 0, 1, 0, 0, 2, 0, 1, 2, 0, 1, 1, 0, 0, 1, 0, 0, 0, 3, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 2, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 3, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0

Offset: 1

Reinhard Zumkeller, Oct 08 2003

nonn

a(n) = 0 for almost all n. The average order of a(n) is 1/log log n. - Charles R Greathouse IV, Apr 29 2012

			a(34)=3, as there are three primes between A001358(34)=19*5=95 and A001358(34+1)=53*2=106: 97, 101 and 103.

T. D. Noe, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Prime Counting Function
Eric Weisstein's World of Mathematics, Semiprime

Cf. A001358, (semiprimes), A088701, A103668 (semiprimes between primes).

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

Select[Range[400], PrimeOmega[#] == 2&] // PrimePi // Differences (* Jean-François Alcover, Oct 12 2021 *)

a(n) = A000720(A001358(n+1)) - A000720(A001358(n));

a(A088701(n)) = n and a(k) <> n for 1 <= k < A088701(n).

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

Original entry on oeis.org

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

Offset: 0

Reinhard Zumkeller, Oct 08 2003

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

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

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 *)

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

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

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

cp's OEIS Frontend

A088700 Number of primes between successive semiprimes.

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