Template:Sequence of the Day for July 10

Intended for: July 10, 2012

Timetable

• First draft entered by Frank Ellerman on April 20, 2011 ✓
• Draft reviewed by Daniel Forgues on July 8, 2011 ✓
• Draft approved by Alonso del Arte on June 9, 2011 ✓

Yesterday's SOTD * Tomorrow's SOTD

The line below marks the end of the <noinclude> ... </noinclude> section.

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A060851:

(2 n  −  1) 3 2 n   − 1, n   ≥   1

.

{ 3, 81, 1215, 15309, 177147, 1948617, ... }

Simon Plouffe published a helpful list of odd zeta values from

ζ  (9)

up to

ζ  (2051)

with a precision of 1000 decimal digits—an older version of this list also covered

ζ  (3)

,

ζ  (5)

and

ζ  (7)

and is now available in separate files with more digits. You could hardwire these values in projects (e.g. RxShell (ZETA and RX.MATH)) where computing small odd

ζ  (2 n  +  1)

values on the fly is no option, because it would take far too long. The odd

ζ  (2 n  +  1)

values can be used to determine Euler’s constant

C0

among other things. A060851 can then help to verify computed values for Euler’s

C0

(usually referred to as

γ

(gamma) or Euler–Mascheroni constant), Apéry’s constant

ζ  (3)

, or log 2 after dynamic changes of the chosen precision, e.g., Open Object Rexx NUMERIC DIGITS 500.