A065414 - OEIS

A065414

Decimal expansion of rank 2 Artin constant Product_{p prime} (1-1/(p^3-p^2)).

6, 9, 7, 5, 0, 1, 3, 5, 8, 4, 9, 6, 3, 6, 5, 9, 0, 3, 2, 8, 4, 6, 7, 0, 3, 5, 0, 8, 2, 0, 9, 2, 2, 9, 2, 4, 0, 7, 3, 1, 5, 3, 9, 4, 6, 2, 1, 4, 5, 1, 5, 3, 9, 5, 3, 5, 4, 3, 7, 8, 7, 5, 2, 8, 8, 6, 4, 5, 9, 1, 1, 0, 5, 9, 6, 0, 9, 5, 5, 6, 6, 6, 6, 6, 1, 5, 4, 8, 3, 8, 5, 1, 3, 0, 7, 1, 8, 7, 9

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,1

REFERENCES

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.4, p. 105.

LINKS

Table of n, a(n) for n=0..98.

R. J. Mathar, Hardy-Littlewood constants embedded into infinite products.., arxiv:0903.2514 [math.NT], 2009-2011, variable A_1^(2).

G. Niklasch, Some number theoretical constants: 1000-digit values. [Cached copy]

Index entries for sequences related to Artin's conjecture.

EXAMPLE

0.697501358496365903284670350820922924...

MATHEMATICA

digits = 99; m0 = 1000; dm = 100; Clear[s]; r[n_] := RootSum[-1 - #^2 + #^3 &, #^n&] - 1; s[m_] := s[m] = NSum[-r[n] PrimeZetaP[n]/n, {n, 3, m}, NSumTerms -> m0, WorkingPrecision -> 300] // Exp; s[m0]; s[m = m0 + dm]; While[RealDigits[s[m], 10, digits][[1]] != RealDigits[s[m - dm], 10, digits][[1]], Print[m]; m = m + dm]; RealDigits[s[m], 10, digits][[1]] (* Jean-François Alcover, Apr 14 2016 *)

PROG

(PARI) prodeulerrat(1-1/(p^3-p^2)) \\ Amiram Eldar, Mar 12 2021

CROSSREFS

Cf. A005596, A065417.

Sequence in context: A145429 A194789 A273082 * A198135 A019813 A096767

Adjacent sequences: A065411 A065412 A065413 * A065415 A065416 A065417

KEYWORD

cons,nonn

AUTHOR

N. J. A. Sloane, Nov 15 2001

STATUS

approved

Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.