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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 (list; constant; graph; refs; listen; history; text; internal format)
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 prime-representing function, Amer. Math. Monthly, 58 (1951), 616-618.

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

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Last modified October 23 20:19 EDT 2017. Contains 293813 sequences.