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%I #7 Dec 24 2015 02:40:01
%S 0,0,1,1,1,1,1,2,2,1,1,2,2,2,1,1,2,2,3,4,4,3,2,2,3,3,3,3,4,5,5,5,5,4,
%T 4,3,4,4,4,3,3,4,5,6,6,5,6,6,7,6,6,6,6,6,6,6,6,6,5,5
%N Number of semiprimes from n to (4/3)*n.
%C a(n) > 0 for all n > 2. a(n) > 1 for all n > 16. This is a semiprime (A001358) related sequence similar to the prime related Bertrand's postulate [1845] that, for n > 1, there is always at least one prime p such that n < p < 2*n. A060715 is the number of primes between n and 2n. A077463 is the number of primes between n and 2n-2.
%H Eric Weisstein et al., <a href="http://mathworld.wolfram.com/BertrandsPostulate.html">Bertrand's Postulate.</a>
%F a(n) = card{S such that S is an element of A001358 and n <= S <= 4*n/3}.
%e a(1) = 0 because there is no semiprime from 1 through 4/3 = 1.3333...
%e a(2) = 0 because there is no semiprime from 2 through 8/3 = 2.6666...
%e a(3) = 1 because there is the semiprime 4 from 3 through 12/3 = 4.
%Y Cf. A001358, A060715, A077463.
%K easy,nonn
%O 1,8
%A _Jonathan Vos Post_, Jan 31 2006