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%I #22 Nov 05 2023 09:02:20
%S 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,
%T 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,
%U 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
%N Number of primes between successive semiprimes.
%C 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
%H T. D. Noe, <a href="/A088700/b088700.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeCountingFunction.html">Prime Counting Function</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Semiprime.html">Semiprime</a>
%F a(n) = A000720(A001358(n+1)) - A000720(A001358(n));
%F a(A088701(n)) = n and a(k) <> n for 1 <= k < A088701(n).
%e 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 Select[Range[400], PrimeOmega[#] == 2&] // PrimePi // Differences (* _Jean-François Alcover_, Oct 12 2021 *)
%Y Cf. A001358, (semiprimes), A088701, A103668 (semiprimes between primes).
%Y Cf. A214520 (primes that are the only prime between consecutive semiprimes).
%K nonn
%O 1,4
%A _Reinhard Zumkeller_, Oct 08 2003
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