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Template:Sequence of the Day for July 10

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Intended for: July 10, 2012


  • 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

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(2 n  −  1) 32 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)
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
among other things. A060851 can then help to verify computed values for Euler’s
(usually referred to as
(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.