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

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, 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, 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

Offset

1,2

Comments

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

References

T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 8.

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..10000 (first 641 terms from Tin Apato)

C. K. Caldwell, Mills's Constant [Gives 6000 terms assuming the Riemann Hypothesis.]

Chris K. Caldwell and Yuanyou Chen, Determining Mills' Constant and a Note on Honaker's Problem, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.1.

Christian Elsholtz, Unconditional Prime-representing Functions, Following Mills, arXiv:2004.01285 [math.NT], 2020.

James Grime and Brady Haran, Awesome Prime Number Constant, Numberphile video (2013).

Brian Hayes, Pumping the Primes, bit-player, Aug 19 2015.

Aminu Alhaji Ibrahim and Sa’idu Isah Abubaka, Aunu Integer Sequence as Non-Associative Structure and Their Graph Theoretic Properties, Advances in Pure Mathematics, 2016, 6, 409-419.

Bernard Montaron, Exponential prime sequences, arXiv:2011.14653 [math.NT], 2020.

Robert P. Munafo, Notable Properties of Specific Numbers

Simon Plouffe, The calculation of p(n) and pi(n), arXiv:2002.12137 [math.NT], 2020.

Kota Saito, Mills' constant is irrational, arXiv:2404.19461 [math.NT], 2024.

László Tóth, A Variation on Mills-Like Prime-Representing Functions, arXiv:1801.08014 [math.NT], 2018.

Eric Weisstein's World of Mathematics, Mills' Constant

Eric Weisstein's World of Mathematics, Prime Formulas

Example

1.3063778838630806904686144926026057129167845851567136443680537599664340537668...

Mathematica

RealDigits[ Nest[ NextPrime[#^3] &, 2, 7]^(1/3^8), 10, 111][[1]] (* Robert G. Wilson v, Nov 14 2012 *)

Prog

(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

Crossrefs

Cf. A051254.

Sequence in context: A212225 A278085 A356195 * A294777 A215664 A088162

Adjacent sequences: A051018 A051019 A051020 * A051022 A051023 A051024

Keyword

nonn,cons

Author

Eric W. Weisstein

Extensions

More terms from Robert G. Wilson v, Sep 08 2000

More terms from Tin Apato (tinapto(AT)yahoo.es), Dec 12 2007

Status

approved