cp's OEIS Frontend

A051021 Decimal expansion of Mills's constant, assuming the Riemann Hypothesis is true.

%I A051021 #94 Apr 17 2025 07:00:45
%S A051021 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 A051021 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 A051021 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 A051021 Decimal expansion of Mills's constant, assuming the Riemann Hypothesis is true.
%C A051021 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 A051021 T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 8.
%D A051021 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.13, p. 130.
%D A051021 Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 137.
%H A051021 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 A051021 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 A051021 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 A051021 Christian Elsholtz, <a href="https://arxiv.org/abs/2004.01285">Unconditional Prime-representing Functions, Following Mills</a>, arXiv:2004.01285 [math.NT], 2020.
%H A051021 James Grime and Brady Haran, <a href="http://www.youtube.com/watch?v=6ltrPVPEwfo">Awesome Prime Number Constant</a>, Numberphile video (2013).
%H A051021 Brian Hayes, <a href="http://bit-player.org/2015/pumping-the-primes">Pumping the Primes</a>, bit-player, Aug 19 2015.
%H A051021 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 A051021 William H. Mills, <a href="http://dx.doi.org/10.1090/S0002-9904-1947-08849-2">A prime-representing function</a>, Bull. Amer. Math. Soc., Vol. 53, No. 6 (1947), p. 604; <a href="https://doi.org/10.1090/S0002-9904-1947-08944-8">Errata</a>, ibid., Vol. 53, No 12 (1947), p. 1196.
%H A051021 Bernard Montaron, <a href="https://arxiv.org/abs/2011.14653">Exponential prime sequences</a>, arXiv:2011.14653 [math.NT], 2020.
%H A051021 Robert P. Munafo, <a href="http://www.mrob.com/pub/math/numbers-2.html">Notable Properties of Specific Numbers</a>.
%H A051021 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 A051021 Kota Saito, <a href="https://arxiv.org/abs/2404.19461">Mills' constant is irrational</a>, arXiv:2404.19461 [math.NT], 2024.
%H A051021 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 A051021 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MillsConstant.html">Mills' Constant</a>.
%H A051021 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeFormulas.html">Prime Formulas</a>.
%e A051021 1.3063778838630806904686144926026057129167845851567136443680537599664340537668...
%t A051021 RealDigits[ Nest[ NextPrime[#^3] &, 2, 7]^(1/3^8), 10, 111][[1]] (* _Robert G. Wilson v_, Nov 14 2012 *)
%o A051021 (PARI) A051021_upto(N=99)=localprec(N+9);digits(10^N*sqrtn(A051254(N=logint(N,3)+2),3^N)\1) \\ _M. F. Hasler_, Sep 11 2024
%Y A051021 Cf. A051254.
%K A051021 nonn,cons
%O A051021 1,2
%A A051021 _Eric W. Weisstein_
%E A051021 More terms from _Robert G. Wilson v_, Sep 08 2000
%E A051021 More terms from Tin Apato (tinapto(AT)yahoo.es), Dec 12 2007