This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A113971 #8 Feb 16 2025 08:32:59
%S A113971 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 A113971 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 A113971 Number of semiprimes from n to (4/3)*n.
%C A113971 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 A113971 Eric Weisstein et al., <a href="https://mathworld.wolfram.com/BertrandsPostulate.html">Bertrand's Postulate.</a>
%F A113971 a(n) = card{S such that S is an element of A001358 and n <= S <= 4*n/3}.
%e A113971 a(1) = 0 because there is no semiprime from 1 through 4/3 = 1.3333...
%e A113971 a(2) = 0 because there is no semiprime from 2 through 8/3 = 2.6666...
%e A113971 a(3) = 1 because there is the semiprime 4 from 3 through 12/3 = 4.
%Y A113971 Cf. A001358, A060715, A077463.
%K A113971 easy,nonn
%O A113971 1,8
%A A113971 _Jonathan Vos Post_, Jan 31 2006