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 A369610 #17 Feb 10 2024 03:00:50
%S A369610 1,1,1,1,3,4,6,7,9,13,14,18,20,21,23,28,32,33,37,40,41,45,47,51,57,60,
%T A369610 61,63,64,67,78,81,85,86,93,94,99,103,105,110,114,115,124,125,127,128,
%U A369610 137,146,148,149,152,157,158,167,171,175,180,181,185,187,188,197,208,211
%N A369610 a(n) is the number of nonprime numbers < prime(n) which are not equal to twice a prime.
%H A369610 Michael De Vlieger, <a href="/A369610/b369610.txt">Table of n, a(n) for n = 1..10000</a>
%F A369610 a(n) = A014689(n) - A079952(n). - _Jinyuan Wang_, Feb 09 2024
%e A369610 a(n) = 1 for n = 1..4 since in each case there is only one nonprime number (1) < prime(n) which is not twice a prime.
%e A369610 a(5) = 3 since prime(5) = 11 and there are precisely 3 nonprime numbers < 11 which are not twice a prime (1,8,9).
%t A369610 nn = Prime[10^4]; c = p = 0; Reap[Do[c += 1 - Boole[PrimeQ[i/2]]; If[PrimeQ[i], p++; Sow[c - p]], {i, nn}]][[-1, 1]] (* _Michael De Vlieger_, Jan 27 2024 *)
%o A369610 (PARI) a369610(n) = {my(s=1); forcomposite (j=4, prime(n)-1, if(j%2!=0 || !isprime(j/2), s++)); s} \\ _Hugo Pfoertner_, Jan 27 2024
%Y A369610 Cf. A000720, A014689, A079952, A100484.
%K A369610 nonn
%O A369610 1,5
%A A369610 _David James Sycamore_, Jan 27 2024