login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A112543 Numerators of fractions n/m in array by antidiagonals. 3

%I

%S 1,2,1,3,1,1,4,3,2,1,5,2,1,1,1,6,5,4,3,2,1,7,3,5,1,3,1,1,8,7,2,5,4,1,

%T 2,1,9,4,7,3,1,2,3,1,1,10,9,8,7,6,5,4,3,2,1,11,5,3,2,7,1,5,1,1,1,1,12,

%U 11,10,9,8,7,6,5,4,3,2,1,13,6,11,5,9,4,1,3,5,2,3,1,1,14,13,4,11,2,3,8,7,2

%N Numerators of fractions n/m in array by antidiagonals.

%C Column m has period m. - _Clark Kimberling_, Jul 04 2013

%C Read as a triangle with antidiagonals for rows, T(n,k) gives the number of distinct locations at which two points the same distance from a center rotating around that center in the same direction at speeds n+1 and k will coincide. - _Thomas Anton_, Nov 23 2018

%H Clark Kimberling, <a href="/A112543/b112543.txt">Antidiagonals n = 1..60, flattened</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ExponentialIntegral.html">Exponential Integral</a>

%F For n/m: g.f.: x/(1-x)*log(1/(1-y)), e.g.f.: x*e^x*(Ei(y)-log(y)+gamma) = x*e^x*integral_t=0^y (e^t-1)dt.

%F n/gcd(m,n). - _Clark Kimberling_, Jul 04 2013

%e a(2,4)=1/2 because 2/4 = 1/2.

%e Northwest corner:

%e 1 2 3 4 5 6 7

%e 1 1 3 2 5 3 7

%e 1 2 1 4 5 2 7

%e 1 1 3 1 5 3 7

%e 1 2 3 4 1 1 7

%e 1 1 1 2 5 1 7

%e 1 2 3 4 5 6 1

%t d[m_, n_] := n/GCD[m, n]; z = 12;

%t TableForm[Table[d[m, n], {m, 1, z}, {n, 1, z}] ] (*array*)

%t Flatten[Table[d[k, m + 1 - k], {m, 1, z}, {k, 1, m}]] (*sequence*)

%t (* _Clark Kimberling_, Jul 04 2013 *)

%o (PARI) t1(n)=binomial(floor(3/2+sqrt(2*n)),2)-n+1 t2(n)=n-binomial(floor(1/2+sqrt(2*n)),2) vector(100,n,t1(n)/gcd(t1(n),t2(n)))

%Y Denominators in A112544. Reduced version of A004736/A002260.

%K easy,frac,nonn,tabl

%O 1,2

%A _Franklin T. Adams-Watters_, Sep 11 2005

%E Keyword tabl added by _Franklin T. Adams-Watters_, Sep 02 2009

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)