Template:Sequence of the Day for October 19

Intended for: October 19, 2012

Timetable

• First draft entered by Alonso del Arte on April 8, 2012 ✓
• Draft reviewed by Daniel Forgues on October 18, 2012 ✓ October 10, 2018 ✓
• Draft to be approved by September 19, 2012

Yesterday's SOTD * Tomorrow's SOTD

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

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A065918: Logarithm of

2 + 2√  3

.

1.3169578969248...

This number figures in the search for Mersenne primes thus: the Mersenne number

M = 2 n  −  1

is prime if and only if

M

divides

     

cosh (2 n  − 2 log (2 + 2√  3  ))  =  e  + { 2 n  − 2 log (2 + 2√  3  ) } + e  − { 2 n  − 2 log (2 + 2√  3  ) } 2  =  (2 + 2√  3  )  + { 2 n  − 2  } + (2 + 2√  3  )  − { 2 n  − 2  } 2  ,

where

cosh (x)

is the hyperbolic cosine function. David Wilson has proposed calling the number

log (2 + 2√  3  )

the Helms constant.
The number

2 + 2√  3 = tan 5 π 12 = cot π 12

is sometimes called the Kasner constant (see A019973 for decimal expansion).