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 A079952 #36 Oct 29 2017 21:29:54
%S A079952 0,0,1,2,3,3,4,4,5,6,6,7,8,8,9,9,10,10,11,11,11,12,13,14,15,15,15,16,
%T A079952 16,16,18,18,19,19,21,21,21,22,23,23,24,24,24,24,25,25,27,29,30,30,30,
%U A079952 30,30,30,31,32,32,32,33,34,34,34,36,36,36,37,38,39,40
%N A079952 Number of primes less than prime(n)/2.
%C A079952 Previous name: Number of primes p such that prime(n) mod 2*p < prime(n).
%C A079952 Same as A055930, except for a(2). [Noticed by _R. J. Mathar_, Dec 15 2008, proved by _Andrey Zabolotskiy_, Oct 26 2017]
%F A079952 A079950(n, a(n) + 1) = prime(n).
%F A079952 Where defined, that is for n > 2, prime(a(n)) = A055377(prime(n)). - _Peter Munn_, Sep 18 2017
%F A079952 0 with partial sums of A217564. - _David A. Corneth_, Oct 26 2017 (found earlier by _Peter Munn_).
%e A079952 n = 6: prime(6) = 13 and 2, 3, 5 are less than 13/2, therefore a(6) = 3.
%t A079952 Table[PrimePi[Prime[n]/2], {n, 75}] (* _Michael De Vlieger_, Sep 20 2017 *)
%o A079952 (PARI) a(n) = primepi(prime(n)/2); \\ _Michel Marcus_, Sep 20 2017
%Y A079952 Cf. A000040, A000720, A055377, A055930, A079951, A079953, A217564.
%K A079952 nonn
%O A079952 1,4
%A A079952 _Reinhard Zumkeller_, Jan 19 2003
%E A079952 New name from _Peter Munn_, Sep 18 2017