

A079614


Decimal expansion of Bertrand's constant.


1



1, 2, 5, 1, 6, 4, 7, 5, 9, 7, 7, 9, 0, 4, 6, 3, 0, 1, 7, 5, 9, 4, 4, 3, 2, 0, 5, 3, 6, 2, 3, 3, 4, 6, 9, 6, 9
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OFFSET

1,2


COMMENTS

From Bertrand's postulate (i.e., there is always a prime p in the range n < p < 2n) one can show there is a constant b such that floor(2^b), floor(2^2^b), ..., floor(2^2^2...^b), ... are all primes.
This result is due to Wright (1951), so Bertrand's constant might be better called Wright's constant, by analogy with Mill's constant A051021.  Jonathan Sondow, Aug 02 2013


REFERENCES

S. Finch, Mathematical Constants, Cambridge Univ. Press, 2003; see section 2.13 Mill's constant.


LINKS

Table of n, a(n) for n=1..37.
C. K. Caldwell, Prime Curios! 137438953481.
Pierre Dusart, Estimates of some functions over primes without R. H., arXiv:1002.0442 [math.NT], 2010.
J. Sondow, E. Weisstein, Bertrand's Postulate
E. M. Wright, A primerepresenting function, Amer. Math. Monthly, 58 (1951), 616618.


FORMULA

1.251647597790463017594432053623346969...


EXAMPLE

2^(2^(2^1.251647597790463017594432053623)) is approximately 37.0000000000944728917062132870071 and A051501(3)=37.


CROSSREFS

Cf. A051021, A051501, A060715.
Sequence in context: A008343 A257264 A093952 * A238387 A084245 A174232
Adjacent sequences: A079611 A079612 A079613 * A079615 A079616 A079617


KEYWORD

cons,hard,more,nonn


AUTHOR

Benoit Cloitre, Jan 29 2003


EXTENSIONS

More digits (from the Prime Curios page) added by Frank Ellermann, Sep 19 2011
a(16)a(37) from Charles R Greathouse IV, Sep 20 2011
Definition clarified by Jonathan Sondow, Aug 02 2013


STATUS

approved



