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

1,3

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

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}]

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

Sequence in context: A337958 A337957 A337956 * A198850 A283120 A209404

Adjacent sequences: A073506 A073507 A073508 * A073510 A073511 A073512

Keyword

base,hard,nonn

Author

Shyam Sunder Gupta, Aug 14 2002

Extensions

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

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

Status

approved