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A131043
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Number of primes between 10^n and 10^n+10^(n-1).
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0
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1, 4, 16, 106, 861, 7216, 61938, 541854, 4814936, 43336106, 394050419, 3612791400
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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 n-th term is R(10^n+10^(n-1))-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.
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LINKS
| Cino Hilliard, Count primes in a range.
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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.
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PROG
| (PARI) /*Some functions*/ pr11(n) = primepi(10^n+10^(n-1))-primepi(10^n) Rpr11(n) = R(10^n+10^(n-1))-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), ", "))
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CROSSREFS
| Sequence in context: A203716 A136793 A009630 * A071554 A087335 A204573
Adjacent sequences: A131040 A131041 A131042 * A131044 A131045 A131046
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KEYWORD
| nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)hotmail.com), Sep 23 2007
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