

A131043


Number of primes between 10^n and 10^n+10^(n1).


1



1, 4, 16, 106, 861, 7216, 61938, 541854, 4814936, 43336106, 394050419, 3612791400, 33353349498, 309745405634, 2891246183239, 27107799609004, 255151905596682, 2409933230413924, 22832347500212719, 216919281298152512, 2066001163137387739, 19721816247905813257
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OFFSET

1,2


COMMENTS

The PARI script is good up to n=9. The last 3 terms were computed by the gcc 4.1.2 program in the link. A good approximation for the nth term is R(10^n+10^(n1))R(10^n) where R(x) is Riemann's approximation of the number of prime numbers < x. This is included in the PARI script. for example, Rpr11(12) = 3612792548.5108.., accurate for the first 6 digits.


LINKS

Table of n, a(n) for n=1..22.
Cino Hilliard, Count primes in a range.
Cino Hilliard, Count primes in a range up to 10^18, message 58 in seqfun Yahoo group, providing code for gcc (needs formatting to become compilable), Sep 23, 2007. [Cached copy]


EXAMPLE

For n=2, the 4 primes in the range 100 to 110 are 101,103,107,109. So 4 is the second entry in the sequence.


PROG

(PARI) /*Some functions*/ pr11(n) = primepi(10^n+10^(n1))primepi(10^n) Rpr11(n) = R(10^n+10^(n1))R(10^(n)) R(x) = local(j); (sum(j=1, 400, moebius(j)*Li(x^(1/j))/j)) /*End functions*/ for(x=1, 9, print1(pr11(x), ", "))


CROSSREFS

Cf. A006880, A309329.
Sequence in context: A274889 A009630 A318695 * A071554 A212313 A332752
Adjacent sequences: A131040 A131041 A131042 * A131044 A131045 A131046


KEYWORD

nonn


AUTHOR

Cino Hilliard, Sep 23 2007


EXTENSIONS

a(13)a(19) from Hugo Pfoertner, Nov 16 2019
a(20)a(21) from Chai Wah Wu, Nov 29 2019
a(22) from Chai Wah Wu, Nov 30 2019


STATUS

approved



