A073510 - OEIS

%I #18 Oct 28 2021 12:59:31

%S 0,2,17,127,1003,8326,71038,618610,5481646,49221187,446590932,

%T 4087194991,37677478288,349465615584,3258501713644,30522628848972,

%U 287059041039078,2709339704446862,25652489700275636,243571629996128384,2318640708958531064,22123070798400775157

%N Number of primes less than 10^n with initial digit 8.

%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)=2 because there are 2 primes up to 10^2 whose initial digit is 8 (namely 83 and 89).

%t f[n_] := f[n] = PrimePi[9*10^n] - PrimePi[8*10^n] + f[n - 1]; f[0] = 0; Table[ f[n], {n, 0, 12}]

%Y A006880(n) = A073509(n)+ ... + A073516(n)+A073517(n-1).

%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