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 A073517 #31 Dec 15 2024 12:58:10
%S A073517 0,4,25,160,1193,9585,80020,686048,6003530,53378283,480532488,
%T A073517 4369582734,40063566855,369893939287,3435376839800,32069022099022,
%U A073517 300694113015105,2830466318006780,26735673312004455,253315661161665338,2406763761677705769,22923886160712831134,218839439542390117580
%N A073517 Number of primes less than 10^n with initial digit 1.
%H A073517 Chris K. Caldwell, <a href="http://www.utm.edu/research/primes/howmany.shtml">How Many Primes Are There?</a>
%H A073517 Xavier Gourdon & Pascal Sebah, <a href="http://numbers.computation.free.fr/Constants/Primes/countingPrimes.html">Counting the number of primes</a>
%H A073517 Henri Lifchitz, <a href="http://ourworld.compuserve.com/homepages/hlifchitz/Henri/us/ParPius.htm">Parity of Pi(n)</a>
%H A073517 Thomas R. Nicely, <a href="https://faculty.lynchburg.edu/~nicely/index.html">Some Results of Computational Research in Prime Numbers</a> [See local copy in A007053]
%H A073517 Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/primes.html">Tables of values of pi(x) and of pi2(x)</a>
%F A073517 a(n) = Sum_{k=0..n-1} pi(2*10^k-1) - pi(10^k-1). - _Andrew Howroyd_, Dec 15 2024
%e A073517 a(2)=4 because there are 4 primes up to 10^2 whose initial digit is 1 (11, 13, 17 and 19).
%t A073517 f[n_] := f[n] = PrimePi[2*10^n] - PrimePi[10^n] + f[n - 1]; f[0] = 0; Table[ f[n], {n, 0, 13}]
%o A073517 (PARI) a(n,d=1)=sum(k=0, n-1, primepi((d+1)*10^k-1) - primepi(d*10^k-1)) \\ _Andrew Howroyd_, Dec 15 2024
%Y A073517 Cf. A000720 (pi), A073509 to A073517, their sum is A006880.
%Y A073517 For primes with initial digit d (1 <= d <= 9) see A045707, A045708, A045709, A045710, A045711, A045712, A045713, A045714, A045715; A073517, A073516, A073515, A073514, A073513, A073512, A073511, A073510, A073509.
%K A073517 base,hard,nonn
%O A073517 1,2
%A A073517 _Shyam Sunder Gupta_, Aug 14 2002
%E A073517 Edited and extended by _Robert G. Wilson v_, Aug 29 2002
%E A073517 a(21)-a(22) added by _David Baugh_, Mar 21 2015
%E A073517 a(23) from _Chai Wah Wu_, Sep 18 2018
%E A073517 Offset corrected by _Andrew Howroyd_, Dec 15 2024