%I #13 Oct 28 2021 12:59:31
%S 1,3,19,139,1097,8960,75290,651085,5735086,51247361,463196868,
%T 4225763390,38851672813,359541975662,3345924530873,31288310624754,
%U 293820812588401,2769490109678920,26191046215879444,248421640738371325,2362546444095790527,22522418647770393663
%N Number of primes less than 10^n with initial digit 3.
%H 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 Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/primes.html">Tables of values of pi(x) and of pi2(x)</a>
%e a(2)=3 because there are 3 primes up to 10^2 whose initial digit is 3 (namely 3, 31 and 37).
%t f[n_] := f[n] = PrimePi[4*10^n] - PrimePi[3*10^n] + f[n - 1]; f[0] = 1; Table[ f[n], {n, 0, 12}]
%Y Cf. A073509 to A073517, their sum is A006880.
%Y 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 nonn,base,hard
%O 1,2
%A _Shyam Sunder Gupta_, Aug 14 2002
%E Edited and extended by _Robert G. Wilson v_, Aug 29 2002
%E a(21)-a(22) added by _David Baugh_, Mar 22 2015