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Editor's Guide

• A239797 Decimal expansion of ${\frac {\sqrt {3}}{\sqrt[{3}]{4}}}$ .
• A238271 Decimal expansion of $\sum _{n=1}^{\infty }{\frac {\mu (n)}{3^{n}}}$ .
• A237042 UPC check digits.
• A236603 Lowest canonical Gray cycles of length $2n$ .
• A235365 Smallest odd prime factor of $3^{n}+1$ .
• A234522 Decimal expansion of ${\sqrt[{4}]{7}}-{\sqrt[{4}]{5}}$ .
• A233748 Number of graphs on n vertices with edges colored with at most four interchangeable colors under the symmetries of the full edge permutation group.
• A232499 Number of unit squares, aligned with a Cartesian grid, completely within the first quadrant of a circle centered at the origin ordered by increasing radius.
• A231963 Concatenate $n$ with its UPC check digit.
• A230624 Numbers $n$ with property that for every base $b\geq 2$ , there is a number $m$ such that $m+s(m)=n$ , where $s(m)$ is the sum of digits in the base $b$ expansion of $m$ .

Sequence of the Day for October 19

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 (2n  − 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).

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On this day...

• October 19, 1675 John Collins writes a letter to James Gregory about John Wallis calculating some lengths on an impossible triangle.
• October 19, 1903 Jean Frédéric Auguste Delsarte born in Fournies.

Sequences in the News

• Dec 25 2018 German Heise-News "integers, please" column explains A003173 and OEIS.
• Feb 01 2018 Alphabet announced a $8,589,869,056 =$A000396(6) stock buyback.
• Jan 03 2018 Largest known term of A000043 announced: 77232917.
• Nov 18 2016 PrimeGrid proves that 10223 is not a Sierpinski number, since 10223 × 2 31172165 + 1 is prime. So no changes to A076336 for now.
• Sep 14 2016 Tom Greer discovers the twin primes 2996863034895 × 2 1290000 ± 1 using PrimeGrid, TwinGen and LLR.
• Jan 19 2016 Largest known term of A000043 announced: 74207281, also discovered by Curtis Cooper.

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