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 A093683 #49 Jan 24 2024 08:01:05
%S A093683 4,25,174,1270,10250,86027,738597,6497407,58047180,524733511,
%T A093683 4789919653,44073509102,408231310520
%N A093683 Number of pairs of twin primes <= 10^n-th prime.
%C A093683 This sequence is >= the values of pi(10^n): 4, 25, 168, 1229, ... in A006880.
%C A093683 a(0) = 0. - _Eduard Roure Perdices_, Dec 23 2022
%D A093683 Enoch Haga, "Wandering through a prime number desert," Table 6, in Exploring prime numbers on your PC and the Internet, 2001 (ISBN 1-885794-17-7).
%H A093683 Soren Laing Aletheia-Zomlefer, Lenny Fukshansky, and Stephan Ramon Garcia, <a href="https://arxiv.org/abs/1807.08899">The Bateman-Horn Conjecture: Heuristics, History, and Applications</a>, arXiv:1807.08899 [math.NT], 2018-2019. See Table 5 p. 40.
%H A093683 Thomas R. Nicely, <a href="https://faculty.lynchburg.edu/~nicely/counts.html">Twin prime count</a>.
%H A093683 <a href="/index/Pri#primepop">Index entries for sequences related to numbers of primes in various ranges</a>
%F A093683 Count twin primes <= p_{10^n}: 10th prime, 100th prime, etc.
%e A093683 a(1) = 4 because there are 4 twin primes <= 29, the 10th prime: (3,5), (5,7), (11,13), and (17,19). (29,31) is not counted because it is not entirely <= 29.
%t A093683 NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; c = 0; p = q = 1; Do[l = Prime[10^n]; While[q <= l, If[p + 2 == q, c++ ]; p = q; q = NextPrim[p]]; Print[c], {n, 12}] (* _Robert G. Wilson v_, Apr 10 2004 *)
%o A093683 (Python)
%o A093683 from sympy import prime, sieve # use primerange for larger terms
%o A093683 def afind(terms):
%o A093683 c, prevp = 0, 1
%o A093683 for n in range(1, terms+1):
%o A093683 for p in sieve.primerange(prevp+1, prime(10**n)+1):
%o A093683 if prevp == p - 2: c += 1
%o A093683 prevp = p
%o A093683 print(c, end=", ")
%o A093683 afind(6) # _Michael S. Branicky_, Apr 25 2021
%Y A093683 See A049035 for another version. - _R. J. Mathar_, Sep 05 2008
%Y A093683 Cf. A006880, A007508.
%K A093683 nonn,more
%O A093683 1,1
%A A093683 _Enoch Haga_, Apr 09 2004
%E A093683 a(9) from _Michael S. Branicky_, Apr 25 2021
%E A093683 a(10) from _Eduard Roure Perdices_, May 08 2021
%E A093683 a(11) from _Eduard Roure Perdices_, Feb 03 2022
%E A093683 a(12) from _Eduard Roure Perdices_, Dec 23 2022
%E A093683 a(13) from _Eduard Roure Perdices_, Jan 24 2024