A073516 Number of primes less than 10^n with initial digit 2.

1, 3, 19, 146, 1129, 9142, 77025, 664277, 5837665, 52064915, 469864125, 4281198201, 39319600765, 363545360347, 3380562309312, 31590949437540, 296487794277035, 2793170342851930, 26402713858800478, 250324979315879678, 2379753569255122805, 22678735843184786383

Offset: 1

Author

Shyam Sunder Gupta, Aug 14 2002

Keywords

• base
• hard
• nonn

Examples

			a(2)=3 because there are 3 primes up to 10^2 whose initial digit is 2 (namely 2, 23 and 29).
		

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[3*10^n] - PrimePi[2*10^n] + f[n - 1]; f[0] = 1; Table[ f[n], {n, 0, 13}]

Extensions

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

a(21)-a(22) added by David Baugh, Mar 21 2015