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User:M. F. Hasler/Proposal for MainPage

 Welcome to the OEIS wiki, the wiki complement to the On-Line Encyclopedia of Integer Sequences. 179,247 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 October 14

A008619:
1 +
 n 2
, n   ≥   0.
(Positive integers repeated twice.)
{ 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, ... }
Smallest positive integer whose harmonic mean with another positive integer is
 n
. For example,
 a (6) = 4
is already given (as 4 is the smallest positive integer such that the harmonic mean of 4 (with 12) is 6) —but the harmonic mean of 2 (with  −  6) is also 6 and 2 < 4, so the two positive integer restrictions need to be imposed to rule out both 2 and  −  6.

Note also that this sequence is the second outermost diagonal of Lozanić’s triangle.

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On this day...

Template:Today in Math History for October 14

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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