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A103669 First occurrence of just n semiprimes occurs between the a(n)-th prime and the next prime.

%I A103669 #4 Mar 30 2012 17:31:12
%S A103669 1,2,4,11,24,34,30,47,221,259,189,375,429,217,1831,1879,1229,3795,
%T A103669 3644,4522,2225,10229,14862,4612,34202,38590,66762,14357,44227,40933,
%U A103669 33608,161441,31545,111924,415069,278832,126172,1576499,104071,271743,786922,3183065,4875380,3166684,2219883,6080675,6443469,1319945
%N A103669 First occurrence of just n semiprimes occurs between the a(n)-th prime and the next prime.
%C A103669 k(31)>78496, k(32)=31545.
%C A103669 The first occurrence of k in A103668. - _Robert G. Wilson v_, May 07 2005
%e A103669 n=3, k=11, p(11)=31, p(12)=37, three semiprimes between 31 and 37 are 33=3*11, 34=2*17,35=5*7.
%t A103669 fQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; f[n_] := Count[fQ /@ Range[Prime[n] + 1, Prime[n + 1] - 1], True];
%t A103669 t = Table[ f[n], {n, 1600000}]; Position[t, #, 1, 1] & /@ Range[0, 41] // Flatten (* Or *) t = Table[0, {50}]; Do[ a = f[n]; If[ t[[a + 1]] == 0, t[[a + 1]] = n], {n, 1600000}]
%Y A103669 Primes: A000040, semiprimes: A001358, number of primes between two successive semiprimes: A088700, number of semiprimes between two successive primes: A103668.
%Y A103669 Cf. A000040, A088700, A001358, A103654, A103655, A103668.
%K A103669 base,nonn
%O A103669 1,2
%A A103669 _Zak Seidov_, Feb 12 2005
%E A103669 More terms from _Robert G. Wilson v_, May 07 2005