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 A111067 #13 Jul 25 2025 09:00:01
%S A111067 1,11,79,427,3009,21779,166649,1322266,10752066,89305602,754868608,
%T A111067 6472917998
%N A111067 Number of odd primes p < 10^n such that p+2 = product of 2 primes (no twin Chen primes).
%C A111067 A006880(n) = number of primes < 10^n, A007508(n) = number of twin primes < 10^n. Let F(n) = A006880(n)/A007508(n). For n > 3, we find that F(n) is ~ 0.762373*log(10^n) - 0.968855.
%C A111067 Let FF(n) = A006880(n)/a(n). For n>3, we find that FF(n) is ~ 0.163128*log(10^n) + 1.349255. a(n)/A007508(n) is then ~ 0.762373*log((10^n) - 0.968855 / ( 0.163128*log(10^n) + 1.349255, as n tends to infinity a(n) / A007508(n) needs to tend to 0.762373 / 0.163128 = 4.673465.
%e A111067 7 is the only prime < 10 with 7+2 = 3*3 = product of 2 odd primes so a(1) = 1.
%t A111067 a[n_] := Count[Prime[Range[2, PrimePi[10^n]]], _?(PrimeOmega[# + 2] == 2 &)]; Array[a, 6] (* _Amiram Eldar_, Jul 25 2025 *)
%o A111067 (PARI) list(len) = {my(c = 0, k = 0, pow = 10); forprime(p = 3, , if(p > pow, print1(c, ", "); k++; if(k == len, break); pow *= 10); if(bigomega(p+2) == 2, c++));} \\ _Amiram Eldar_, Jul 25 2025
%Y A111067 Cf. A006880, A007508, A063637.
%K A111067 nonn,hard,more
%O A111067 1,2
%A A111067 _Pierre CAMI_, Oct 08 2005
%E A111067 a(8) corrected and a(9) computed by _Robert G. Wilson v_, Oct 10 2005
%E A111067 a(10)-a(12) from _Amiram Eldar_, Jul 25 2025