A073512 Number of primes less than 10^n with initial digit 6.

0, 2, 18, 135, 1013, 8458, 72257, 628206, 5556434, 49815418, 451476802, 4128049326, 38024311091, 352446754137, 3284400373590, 30749731897370, 289066731934716, 2727216210298152, 25812680778645432, 245015325044029789, 2331718909954888809, 22242097596092999144

Offset: 1

Author

Shyam Sunder Gupta, Aug 14 2002

Keywords

• base
• hard
• nonn

Examples

			a(2)=2 because there are 2 primes up to 10^2 whose initial digit is 2 (namely 61 and 67).
		

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

Cf. A073509 to A073517, their sum is A006880.

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[7*10^n] - PrimePi[6*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