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%I #79 May 01 2024 02:59:09
%S 1,3,0,6,3,7,7,8,8,3,8,6,3,0,8,0,6,9,0,4,6,8,6,1,4,4,9,2,6,0,2,6,0,5,
%T 7,1,2,9,1,6,7,8,4,5,8,5,1,5,6,7,1,3,6,4,4,3,6,8,0,5,3,7,5,9,9,6,6,4,
%U 3,4,0,5,3,7,6,6,8,2,6,5,9,8,8,2,1,5,0,1,4,0,3,7,0,1,1,9,7,3,9,5,7,0,7,2,9
%N Decimal expansion of Mills's constant, assuming the Riemann Hypothesis is true.
%C Not known to be rational or irrational. See Saito (2024) for a new result. - _Charles R Greathouse IV_, Jul 18 2013, _Hugo Pfoertner_, May 01 2024
%D T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 8.
%H Robert G. Wilson v, <a href="/A051021/b051021.txt">Table of n, a(n) for n = 1..10000</a> (first 641 terms from Tin Apato)
%H C. K. Caldwell, <a href="https://t5k.org/glossary/page.php?sort=MillsConstant">Mills's Constant</a> [Gives 6000 terms assuming the Riemann Hypothesis.]
%H Chris K. Caldwell and Yuanyou Chen, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL8/Caldwell/caldwell78.html">Determining Mills' Constant and a Note on Honaker's Problem</a>, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.1.
%H Christian Elsholtz, <a href="https://arxiv.org/abs/2004.01285">Unconditional Prime-representing Functions, Following Mills</a>, arXiv:2004.01285 [math.NT], 2020.
%H James Grime and Brady Haran, <a href="http://www.youtube.com/watch?v=6ltrPVPEwfo">Awesome Prime Number Constant</a>, Numberphile video (2013).
%H Brian Hayes, <a href="http://bit-player.org/2015/pumping-the-primes">Pumping the Primes</a>, bit-player, Aug 19 2015.
%H Aminu Alhaji Ibrahim and Sa’idu Isah Abubaka, <a href="http://dx.doi.org/10.4236/apm.2016.66028">Aunu Integer Sequence as Non-Associative Structure and Their Graph Theoretic Properties</a>, Advances in Pure Mathematics, 2016, 6, 409-419.
%H Bernard Montaron, <a href="https://arxiv.org/abs/2011.14653">Exponential prime sequences</a>, arXiv:2011.14653 [math.NT], 2020.
%H Robert P. Munafo, <a href="http://www.mrob.com/pub/math/numbers-2.html">Notable Properties of Specific Numbers</a>
%H Simon Plouffe, <a href="https://arxiv.org/abs/2002.12137">The calculation of p(n) and pi(n)</a>, arXiv:2002.12137 [math.NT], 2020.
%H Kota Saito, <a href="https://arxiv.org/abs/2404.19461">Mills' constant is irrational</a>, arXiv:2404.19461 [math.NT], 2024.
%H László Tóth, <a href="https://arxiv.org/abs/1801.08014">A Variation on Mills-Like Prime-Representing Functions</a>, arXiv:1801.08014 [math.NT], 2018.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MillsConstant.html">Mills' Constant</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeFormulas.html">Prime Formulas</a>
%e 1.3063778838630806904686144926026057129167845851567136443680537599664340537668...
%t RealDigits[ Nest[ NextPrime[#^3] &, 2, 7]^(1/3^8), 10, 111][[1]] (* _Robert G. Wilson v_, Nov 14 2012 *)
%Y Cf. A051254.
%K nonn,cons
%O 1,2
%A _Eric W. Weisstein_
%E More terms from _Robert G. Wilson v_, Sep 08 2000
%E More terms from Tin Apato (tinapto(AT)yahoo.es), Dec 12 2007
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