A073515 Number of primes less than 10^n with initial digit 3.

1, 3, 19, 139, 1097, 8960, 75290, 651085, 5735086, 51247361, 463196868, 4225763390, 38851672813, 359541975662, 3345924530873, 31288310624754, 293820812588401, 2769490109678920, 26191046215879444, 248421640738371325, 2362546444095790527, 22522418647770393663

Offset

1,2

Links

Table of n, a(n) for n=1..22.

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)

Example

a(2)=3 because there are 3 primes up to 10^2 whose initial digit is 3 (namely 3, 31 and 37).

Mathematica

f[n_] := f[n] = PrimePi[4*10^n] - PrimePi[3*10^n] + f[n - 1]; f[0] = 1; Table[ f[n], {n, 0, 12}]

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

Sequence in context: A115750 A156894 A221374 * A074559 A027314 A025571

Adjacent sequences: A073512 A073513 A073514 * A073516 A073517 A073518

Keyword

nonn,base,hard

Author

Shyam Sunder Gupta, Aug 14 2002

Extensions

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

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

Status

approved