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 Welcome to the OEIS wiki, the wiki complement to the On-Line Encyclopedia of Integer Sequences. 179,148 articles.

## Editor's Guide

• A239797 Decimal expansion of ${\displaystyle {\frac {\sqrt {3}}{\sqrt[{3}]{4}}}}$.
• A238271 Decimal expansion of ${\displaystyle \sum _{n=1}^{\infty }{\frac {\mu (n)}{3^{n}}}}$.
• A237042 UPC check digits.
• A236603 Lowest canonical Gray cycles of length ${\displaystyle 2n}$.
• A235365 Smallest odd prime factor of ${\displaystyle 3^{n}+1}$.
• A234522 Decimal expansion of ${\displaystyle {\sqrt[{4}]{7}}-{\sqrt[{4}]{5}}}$.
• 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 ${\displaystyle n}$ with its UPC check digit.
• A230624 Numbers ${\displaystyle n}$ with property that for every base ${\displaystyle b\geq 2}$, there is a number ${\displaystyle m}$ such that ${\displaystyle m+s(m)=n}$, where ${\displaystyle s(m)}$ is the sum of digits in the base ${\displaystyle b}$ expansion of ${\displaystyle m}$.

## Sequence of the Day for June 22

A060294: Decimal expansion of Buffon’s constant
 2 π
.
0.63661977236758...
Theorem (Buffon’s needle problem, problem first posed in 1733, solved in 1777). (Georges-Louis Leclerc, Comte de Buffon)

The probability
 P (l, d )
that a needle of length
 l
will randomly land on a line, given a floor with equally spaced parallel lines at a distance
 d   ≥   1
apart, is
P (l, d ) =
 2 π
⋅
 l d

.

Proof. (assuming that the angle and the position of the fallen needle are independently and uniformly random) If the needle always fell perpendicular (angle
θ =
 π 2
radians) to the parallel lines, we would have
P(l, d ) =
 l d

. So we have
P (l, d ) =
 π 0
sin θ   ⋅
 d θ π
⋅  P(l, d ) =
 − [cos θ  ] π0 π
⋅
 l d
=
 2 π
⋅
 l d
.
□

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## On this day...

• June 22, 1850 Count Libri is convicted in France in absentia of stealing valuable books on scientific and mathematical topics.
• June 22, 1925 Felix Klein dies in Göttingen.
• June 22, 1993 At Cambridge, Andrew Wiles gives the second of three lectures about Fermat's last theorem.

## Sequences in the News

• 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: 274207281, also discovered by Curtis Cooper.
• Mar 02 2014 Fredrik Johansson announces a computation of the partition number p(10 20) ≈ 1.8381765 × 10 11140086259, the largest known term of A000041.
• Dec 06 2013 Microsoft launches a challenge to find large non-Mersenne primes, A138837.

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