login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A306340 Decimal expansion of lambda(7) in Li's criterion. 15
1, 1, 2, 4, 4, 6, 0, 1, 1, 7, 5, 7, 0, 9, 5, 9, 4, 9, 0, 5, 8, 2, 8, 2, 0, 1, 0, 8, 0, 1, 6, 9, 7, 5, 6, 4, 0, 4, 5, 9, 7, 7, 0, 9, 4, 3, 2, 3, 1, 3, 8, 3, 1, 4, 1, 2, 4, 8, 4, 0, 7, 6, 1, 5, 5, 8, 3, 7, 4, 2, 3, 1, 1, 5, 4, 6, 1, 5, 6, 0, 2, 7, 2, 4, 9, 6, 2, 9, 9, 6, 4, 9, 9, 1, 3, 4, 9, 0, 1, 2, 7, 0, 3, 9, 8, 6, 9, 9, 0, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..110.

E. Bombieri and J. C. Lagarias, Complements to Li's Criterion for the Riemann Hypothesis, J. Number Th. 77(2) (1999), 274-287.

M. W. Coffey, Relations and positivity results for derivatives of the Riemann xi function, J. Comput. Appl. Math. 166(2) (2004), 525-534.

Xian-Jin Li, The positivity of a sequence of numbers and the Riemann hypothesis, J. Number Th. 65(2) (1997), 325-333.

Eric Weisstein's World of Mathematics, Li's Criterion.

Eric Weisstein's World of Mathematics, Riemann Zeta Function Zeros.

Wikipedia, Li's criterion.

EXAMPLE

1.124460117570959490...

MATHEMATICA

RealDigits[With[{e = EulerGamma, g = StieltjesGamma}, 1 + 7 e/2 - 21 e^2 + 35 e^3 - 35 e^4 + 21 e^5 - 7 e^6 + e^7 + 21 Pi^2/8 + 35 Pi^4/96 + 7 Pi^6/960 - 42 g[1] + 105 e g[1] - 140 e^2 g[1] + 105 e^3 g[1] - 42 e^4 g[1] + 7 e^5 g[1] - 70 g[1]^2 + 105 e g[1]^2 - 63 e^2 g[1]^2 + 14 e^3 g[1]^2 - 14 g[1]^3 + 7 e g[1]^3 + 105 g[2]/2 - 70 e g[2] + 105/2 e^2 g[2] - 21 e^3 g[2] + 7/2 e^4 g[2] + 105/2 g[1] g[2] - 42 e g[1] g[2] + 21/2 e^2 g[1] g[2] + 7/2 g[1]^2 g[2] - 21 g[2]^2/4 + 7/4 e g[2]^2 - 70 g[3]/3 + 35/2 e g[3] - 7 e^2 g[3] + 7/6 e^3 g[3] - 7 g[1] g[3] + 7/3 e g[1] g[3] + 7/12 g[2] g[3] + 35 g[4]/8 - 7/4 e g[4] + 7/24 e^2 g[4] + 7/24 g[1] g[4] - 7 g[5]/20 + 7/120 e g[5] + 7 g[6]/720 - 7/2 Log[4 Pi] - 245 Zeta[3]/8 - 651 Zeta[5]/32 - 127 Zeta[7]/128], 10, 110][[1]]

CROSSREFS

Cf. A074760 (lambda_1), A104539 (lambda_2), A104540 (lambda_3).

Cf. A104541 (lambda_4), A104542 (lambda_5), A306339 (lambda_6), A306341 (lambda_8).

Sequence in context: A243003 A223227 A160904 * A205969 A326771 A049782

Adjacent sequences:  A306337 A306338 A306339 * A306341 A306342 A306343

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Feb 08 2019

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 29 18:25 EDT 2022. Contains 354913 sequences. (Running on oeis4.)