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  • A238271 Decimal expansion of .
  • A237042 UPC check digits.
  • A236603 Lowest canonical Gray cycles of length .
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  • A234522 Decimal expansion of .
  • 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.
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  • A231963 Concatenate with its UPC check digit.
  • A230624 Numbers with property that for every base , there is a number such that , where is the sum of digits in the base expansion of .


Sequence of the Day

Sequence of the Day for June 22

A060294: Decimal expansion of Buffon’s constant
2
π
.
0.63661977236758...

Buffon’s needle problem:

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   ⋅  
dθ
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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