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User:M. F. Hasler/Proposal for MainPage

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  • A239797 Decimal expansion of .
  • A238271 Decimal expansion of .
  • A237042 UPC check digits.
  • A236603 Lowest canonical Gray cycles of length .
  • A235365 Smallest odd prime factor of .
  • 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.
  • 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 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 21

a (n) = n
, the arithmetic derivative of
n: a (0) = a (1) = 0, a ( prime) = 1, a (mn) = m  a (n) + n  a (m)
{ 0, 0, 1, 1, 4, 1, 5, 1, 12, 6, 7, 1, 16, ... }
Based on the product rule for differentiation of functions: for functions
f  (x)
g (x)
( fg ) = fg + fg
. So with numbers,
(ab) = ab + ab
. This implies
1 = 0

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On this day...

  • June 21, 1781 Siméon Denis Poisson is born in Pithivers.
  • June 21, 1809 Released from an Algerian penal colony, François Arago boards a third ship headed to Marseille, hoping to resume his work measuring the meridian.
  • June 21, 1993 At Cambridge, Andrew Wiles gives the first of three lectures about Fermat's last theorem.

Sequences in the news

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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