cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A092802 Mean (rounded) of composite numbers below 10^n.

Original entry on oeis.org

7, 53, 510, 5047, 50279, 501844, 5012809, 50094049, 500720912, 5005703554, 50046261712, 500382762350, 5003219541311, 50027458290511, 500236958622730, 5002065769284422, 50018168989895296, 500161047150051653, 5001437349858735047, 50012907314623137795, 500116546694296773760
Offset: 1

Views

Author

Enoch Haga, Mar 06 2004

Keywords

Comments

As with the primes in A092800, each succeeding term seems a close multiple of that preceding.

Examples

			a(3) = 510 because the mean of composites below 10^3 is 510.087... .

Links

Crossrefs

Cf. A092800, A092801.

Formula

Add composites and divide total by the count of composites below 10^n.
a(n) = floor((10^n(10^n + 1)/2 - A046731(n) - 1)/(10^n - A006880(n) - 1)). - Charles R Greathouse IV, Sep 25 2008

Extensions

More terms from Charles R Greathouse IV, Sep 25 2008

A092871 Number of composites < 10^n.

Original entry on oeis.org

0, 4, 73, 830, 8769, 90406, 921500, 9335419, 94238543, 949152464, 9544947487, 95881945185, 962392087980, 9653934463159, 96795058249196, 970155429577329, 9720761658966073, 97376442842345765, 975260045712259138, 9765942332723655391, 97779180397439081158
Offset: 0

Views

Author

Enoch Haga, Mar 08 2004

Keywords

Comments

The number 1 is omitted from the count as it is neither prime nor composite

Examples

			10^3 = 1000. 1000-2 = 998. a(3) = 830 because the 830 composites+168 primes must total 998.

Links

Crossrefs

Cf. A065894, A006880, A092801, A092802.

Programs

  • Mathematica
    Table[10^i-PrimePi[10^i]-2,{i,14}] (* Harvey P. Dale, Oct 01 2011 *) (* Mathematica's implementation of PrimePi does not work for 10^15 or above *)

Formula

For n>0, a(n) = A065894(n) - 1 = 10^n - 2 - A006880(n). - Max Alekseyev, Aug 15 2013

Extensions

Edited by Max Alekseyev, Aug 15 2013

A091716 Standard deviation (rounded) of primes below 10^n.

Original entry on oeis.org

2, 29, 298, 2962, 29412, 292821, 2921863, 29170821, 291324189, 2910238255, 29078387910, 290589147156, 2904276036695
Offset: 1

Views

Author

Enoch Haga, Mar 05 2004

Keywords

Comments

It appears that a good estimate for the standard deviation of primes below 10^(n+1) is about 10 times the term for 10^n.
Heuristically, if we use a model where each positive integer x has probability approximately 1/log(x) of being prime, we should expect the standard deviation of the primes below N to be approximately N/sqrt(12). - Robert Israel, Sep 23 2014

Examples

			a(6) = 292821 (rounded from 292820.634) because this is the computed and rounded sample standard deviation of the 78498 primes below 10^6.

References

  • John E. Freund, Modern elementary statistics, 5th ed. (Prentice-Hall, 1979), pp. 42-47

Crossrefs

Cf. A092800, A092801, A092802.

Programs

  • Maple
    seq(round(Statistics:-StandardDeviation(select(isprime, [$2 .. 10^n-1]))),n=1..7); # Robert Israel, Sep 23 2014

Extensions

a(9)-a(13) from Hiroaki Yamanouchi, Sep 23 2014
Showing 1-3 of 3 results.

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