login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A099473 Numbers k such that binomial(2*k,k) cannot be represented as the sum of three squares. 2

%I #14 Sep 29 2020 04:06:57

%S 5,6,12,24,27,30,39,48,57,60,71,85,86,90,96,106,111,113,119,120,123,

%T 126,135,159,172,180,192,212,225,240,249,252,263,287,293,294,297,306,

%U 329,344,347,350,360,363,365,378,384,402,424,427,429,437,438,447,449,479

%N Numbers k such that binomial(2*k,k) cannot be represented as the sum of three squares.

%C Granville and Zhu show that the density of these numbers is 1/8.

%H Amiram Eldar, <a href="/A099473/b099473.txt">Table of n, a(n) for n = 1..10000</a>

%H Andrew Granville and Yiliang Zhu, <a href="http://jstor.org/stable/2323831">Representing binomial coefficients as sums of squares</a>, Amer. Math. Monthly, Vol. 97, No. 6 (1990), pp. 486-493; <a href="http://www.dms.umontreal.ca/~andrew/PDF/YZhu.pdf">alternative link</a>.

%t NoRepAs3Sqrs[n_] := Module[{e2}, e2=IntegerExponent[n, 2]; If[EvenQ[e2], 7==Mod[n/2^e2, 8], False]]; Select[Range[500], NoRepAs3Sqrs[Binomial[2#, # ]]&]

%Y Cf. A004215 (sums of 4 but no fewer nonzero squares), A099472.

%K nonn

%O 1,1

%A _T. D. Noe_, Oct 18 2004

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)