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A073517 Number of primes less than 10^n with initial digit 1. 23
0, 4, 25, 160, 1193, 9585, 80020, 686048, 6003530, 53378283, 480532488, 4369582734, 40063566855, 369893939287, 3435376839800, 32069022099022, 300694113015105, 2830466318006780, 26735673312004455, 253315661161665338, 2406763761677705769, 22923886160712831134, 218839439542390117580 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..22.

Chris K. Caldwell, How Many Primes Are There?

Xavier Gourdan & Pascal Sebah, Counting the number of primes

Henri Lifchitz, Parity of Pi(n)

Thomas R. Nicely, Some Results of Computational Research in Prime Numbers

Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

EXAMPLE

a(2)=4 because there are 4 primes up to 10^2 whose initial digit is 1 (11, 13, 17 and 19).

MATHEMATICA

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

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: A079750 A195510 A264775 * A208264 A184755 A074422

Adjacent sequences:  A073514 A073515 A073516 * A073518 A073519 A073520

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(21) added by David Baugh, Mar 21 2015

a(22) from Chai Wah Wu, Sep 18 2018

STATUS

approved

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Last modified February 23 05:58 EST 2019. Contains 320411 sequences. (Running on oeis4.)