login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A233825 Decimal expansion of Nicolas's constant in his condition for the Riemann Hypothesis (RH). 3
3, 6, 4, 4, 4, 1, 5, 0, 9, 6, 4, 0, 7, 3, 7, 0, 1, 4, 1, 0, 6, 5, 1, 1, 6, 1, 9, 2, 8, 3, 5, 1, 4, 8, 1, 6, 0, 0, 5, 2, 2, 6, 0, 2, 4, 6, 6, 4, 3, 2, 4, 2, 4, 5, 6, 8, 5, 2, 4, 6, 3, 7, 5, 8, 2, 6, 3, 7, 4, 1, 7, 3, 4, 8, 0, 9, 2, 9, 5, 8, 1, 8, 6, 8, 3, 2, 3, 0, 5, 7, 0, 5, 1, 7, 5, 1, 2, 6, 1, 6, 1, 5, 5, 6, 4, 1, 4, 3, 3, 5, 5, 3, 1, 7, 7, 5, 2, 9, 2, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

e^gamma*(4 + gamma - log(4*pi)), where gamma is the Euler-Mascheroni constant.

e^gamma*(2 + beta), where beta = sum 1/(rho*(1-rho)), where rho runs over all nonreal zeros of the zeta function.

Nicolas proved that RH is true if and only if limsup_{n-->infinity} (n/phi(n) - e^gamma*log(log(n)))*sqrt(log(n)) = e^gamma*(4 + gamma - log(4*pi)), where phi(n) = A000010(n).

LINKS

Table of n, a(n) for n=1..120.

J. Lagarias, Euler's constant: Euler's work and modern developments, Bull. A.M.S., 50 (2013), 527-628; see p. 574.

J.-L. Nicolas, Small values of the Euler function and the Riemann hypothesis, Acta Arith., 155 (2012), 311-321.

EXAMPLE

3.64441509640737014106511619283514816005226024664324245685246375826374...

PROG

(PARI) exp(Euler)*(4 + Euler - log(4*pi)) \\ Charles R Greathouse IV, Mar 10 2016

CROSSREFS

Cf. A195423, A216868, A218245.

Sequence in context: A090038 A308291 A006464 * A159354 A196500 A023676

Adjacent sequences:  A233822 A233823 A233824 * A233826 A233827 A233828

KEYWORD

nonn,cons

AUTHOR

Jonathan Sondow, Dec 19 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 17 12:37 EST 2020. Contains 330958 sequences. (Running on oeis4.)