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A073517
Number of primes less than 10^n with initial digit 1.
24
0, 4, 25, 160, 1193, 9585, 80020, 686048, 6003530, 53378283, 480532488, 4369582734, 40063566855, 369893939287, 3435376839800, 32069022099022, 300694113015105, 2830466318006780, 26735673312004455, 253315661161665338, 2406763761677705769, 22923886160712831134, 218839439542390117580
OFFSET
0,2
LINKS
Chris K. Caldwell, How Many Primes Are There?
Xavier Gourdon & Pascal Sebah, Counting the number of primes
Henri Lifchitz, Parity of Pi(n)
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 A357162 A184755
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