A065415 - OEIS

A065415

Decimal expansion of Product_{p prime} (1-1/(p^4-p^3)).

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

(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 over all positive integers, arXiv:0903.2514 [math.NT], 2009-2011, constant A_1^(3) table 3.

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

EXAMPLE

0.85654044485354217442616798413595388...

MATHEMATICA

digits = 99; $MaxExtraPrecision = 400; m0 = 1000; dm = 100; Clear[s]; LR = LinearRecurrence[{2, -1, 0, 1, -1}, {0, 0, 0, 4, 5, 6}, 2 m0]; r[n_Integer] := LR[[n]]; s[m_] := s[m] = NSum[-r[n] PrimeZetaP[n]/n, {n, 3, m}, NSumTerms -> m0, WorkingPrecision -> 400] // 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 15 2016 *)

PROG

(PARI) prodeulerrat(1-1/(p^4-p^3)) \\ Amiram Eldar, Mar 13 2021

CROSSREFS

Cf. A005596, A065414, A065416.

Sequence in context: A190412 A199615 A199059 * A154013 A230152 A099002

Adjacent sequences: A065412 A065413 A065414 * A065416 A065417 A065418

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.