%I #11 Oct 28 2021 12:59:31

%S 0,3,20,139,1069,8747,74114,641594,5661135,50653546,458352691,

%T 4185483176,38510936699,356622729564,3320632228693,31067060521057,

%U 291869049531878,2752144407792176,26035873192178041,247025281876786013,2349914303292170310,22407593754131275705

%N Number of primes less than 10^n with initial digit 4.

%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 4 (namely 41, 43 and 47).

%t f[n_] := f[n] = PrimePi[5*10^n] - PrimePi[4*10^n] + f[n - 1]; f[0] = 0; Table[ f[n], {n, 0, 13}]

%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 base,hard,nonn

%O 1,2

%A _Shyam Sunder Gupta_, Aug 14 2002

%E Edited and extended by _Robert G. Wilson v_, Aug 29 2002

%E a(20)-a(22) added by _David Baugh_, Mar 22 2015