A073509 Number of primes less than 10^n with initial digit 9.

0, 1, 15, 127, 1006, 8230, 70320, 614821, 5453140, 48982456, 444608278, 4070532710, 37535715441, 348245215460, 3247889171908, 30429496751905, 286235215995588, 2702000272361599, 25586688305447928, 242978340446949438, 2313264023790027111, 22074118786158858975

Offset: 1

Author

Shyam Sunder Gupta, Aug 14 2002

Keywords

• base
• hard
• nonn

Examples

			a(2) = 1 because there is 1 prime less than 100 whose initial digit is 9, i.e., 97.
		

Links

• Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
• Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Crossrefs

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

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

Programs

Mathematica

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

Extensions

Edited and extended by Robert G. Wilson v, Aug 29 2002

a(20)-a(22) added by David Baugh, Mar 22 2015