cp's OEIS Frontend

A079614 Decimal expansion of Bertrand's constant.

%I A079614 #56 Feb 16 2025 08:32:48
%S A079614 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,
%T A079614 9,6,9
%N A079614 Decimal expansion of Bertrand's constant.
%C A079614 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.
%C A079614 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
%D A079614 S. Finch, Mathematical Constants, Cambridge Univ. Press, 2003; see section 2.13 Mills's constant.
%H A079614 C. K. Caldwell, <a href="https://t5k.org/curios/page.php/137438953481.html">Prime Curios! 137438953481</a>.
%H A079614 Pierre Dusart, <a href="http://arxiv.org/abs/1002.0442">Estimates of some functions over primes without R. H.</a>, arXiv:1002.0442 [math.NT], 2010.
%H A079614 J. Sondow, E. Weisstein, <a href="https://mathworld.wolfram.com/BertrandsPostulate.html">Bertrand's Postulate</a>.
%H A079614 E. M. Wright, <a href="http://www.jstor.org/stable/2306356">A prime-representing function</a>, Amer. Math. Monthly, 58 (1951), 616-618.
%F A079614 1.251647597790463017594432053623346969...
%e A079614 2^(2^(2^1.251647597790463017594432053623)) is approximately 37.0000000000944728917062132870071 and A051501(3)=37.
%Y A079614 Cf. A051021, A051501, A060715.
%K A079614 cons,hard,more,nonn
%O A079614 1,2
%A A079614 _Benoit Cloitre_, Jan 29 2003
%E A079614 More digits (from the Prime Curios page) added by _Frank Ellermann_, Sep 19 2011
%E A079614 a(16)-a(37) from _Charles R Greathouse IV_, Sep 20 2011
%E A079614 Definition clarified by _Jonathan Sondow_, Aug 02 2013