A079614 Decimal expansion of Bertrand's constant.

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

Offset: 1

Author

Benoit Cloitre, Jan 29 2003

Keywords

• cons
• hard
• more
• nonn

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 Mills's constant A051021. - Jonathan Sondow, Aug 02 2013

Examples

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

References

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

Links

• 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.

Crossrefs

Cf. A051021, A051501, A060715.

Formula

1.251647597790463017594432053623346969...

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