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 A269233 #18 Mar 11 2016 05:12:12
%S A269233 0,0,3,2,1,1,5,2,2,8,1,5,12,46,20,5,1,1,22,17,31,3,51,2,7,20,32,8,10,
%T A269233 45,17,56,93,59,5,8,31,20,1,13,57,17,44,80,3,27,88,59,3,92,198,34,34,
%U A269233 40
%N A269233 a(n) = number of "candidate primes" < A037053(n). (See Comments for description and explanation.)
%C A269233 A037053(n) = the smallest prime containing exactly n zeros. After A037053(0)=2, the smallest possible terms ("candidate primes") in A037053 are of the form a[n zeros]b, a in {1..9}, b in {1,3,7,9}; the first such being 1[n zeros]1. These are followed by forms 1[n zeros]ab, 1[n-k zeros]a[k zeros]b {k=1..n}, then {2..9}[n-k zeros]a[k zeros]b, etc. The present sequence represents the number of smaller candidates which are excluded before a prime occurs. See Examples below and A037053 for additional details.
%C A269233 These numbers will never appear: 12k+4, 12k+6, 12k+9, 12k+11, for k = 0 to 2, and 12k, 12k+2, 12k+5, 12k+7, for k > 2. - _Hans Havermann_, Feb 23 2016
%C A269233 Additionally, 26 will never appear. - _Hans Havermann_, Mar 10 2016
%e A269233 a(1)=0 because the smallest possible (candidate) prime containing one zero is 101, which is prime.
%e A269233 a(6)=5 because A037053(6)=20000003; the five smaller candidates {10000001, 10000003, 10000007, 10000009, 20000001} are composite.
%e A269233 a(13)=46 because A037053(13)=1000000000000037; the 36 smaller candidates of the form {1..9}[13 zeros]{1,3,7,9} are composite, as are the 10 candidates 1[13 zeros]{1,2}{1,3,7,9} and 1[13 zeros]3{1,3}.
%Y A269233 Cf. A037053, A270095 (records).
%K A269233 nonn,base
%O A269233 0,3
%A A269233 _Bob Selcoe_, Feb 20 2016
%E A269233 Corrected a(15) & fixed Example typo. - _Hans Havermann_, Feb 21 2016