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, 1, 6, 3, 6, 4, 6, 3, 2, 9

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

References

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

Links

Table of n, a(n) for n=1..46.

Chris K. Caldwell, Prime Curios! 137438953481.

Pierre Dusart, Estimates of some functions over primes without R. H., arXiv:1002.0442 [math.NT], 2010.

Pierre Dusart, Explicit estimates of some functions over primes, Ramanujan J. 45 (2018), 227-251.

Jonathan Sondow and Eric Weisstein, Bertrand's Postulate.

Wikipedia, Bertrand's postulate.

E. M. Wright, A prime-representing function, Amer. Math. Monthly, 58 (1951), 616-618.

Formula

1.251647597790463017594432053623346969163646329...

Example

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

Crossrefs

Cf. A051021, A051501, A060715.

Sequence in context: A257264 A093952 A308882 * 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

a(38)-a(46) from Martin Fuller, Apr 18 2026

Status

approved