A073511 Number of primes less than 10^n with initial digit 7.

1, 4, 18, 125, 1027, 8435, 71564, 622882, 5516130, 49495432, 448855139, 4106164356, 37838546363, 350849788546, 3270531245684, 30628143485953, 287992070079777, 2717649138419586, 25726964404879666, 244242934202964444, 2324722877951987037, 22178433287546997612

Offset: 1

Author

Shyam Sunder Gupta, Aug 14 2002

Keywords

• base
• hard
• nonn

Examples

			a(2)=4 because there are 4 primes up to 10^2 whose initial digit is 7 (namely 7, 71, 73 and 79).
		

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[8*10^n] - PrimePi[7*10^n] + f[n - 1]; f[0] = 1; 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