A175244 - OEIS

%I #2 Mar 30 2012 17:35:35

%S 1,1,1,1,1,1,2,1,2,1,1,2,1,1,1,2,2,2,3,1,3,1,1,3,1,1,1,3,2,3,1,2,3,1,

%T 1,2,3,4,1,4,1,1,4,1,1,1,4,2,4,1,2,4,1,1,2,4,1,1,1,2,4,2,2,4,5,1,5,1,

%U 1,5,1,1,1,5,2,5,1,2,5,1,1,2,5,1,1,1,2,5,2,2,5,3,5

%N For k>=1 let k = a(i)^2 +...+ a(i+r-1)^2, r is the least number of squares that add up to k (A002828); a(i)<=a(i+1)<=..<=a(i+r-1); i>=1.

%e 1=1^2 so a(1)=1, 2=1^2+1^2 so a(2)=1 and a(3)=1, 3=1^2+1^2+1^2 so a(4)=1 and a(5)=1 and a(6)=1, 4=2^2 so a(7)=2, 5=1^2+2^2 so a(8)=1 and a(9)=2, 6=1^2+1^2+2^2 so a(10)=1 and a(11)=1 and a(12)=2, 7=1^2+1^2+1^2+2^2 so a(13)=1 and a(14)=1 and a(15)=1 and a(16)=2, 8=2^2+2^2 so a(17)=2 and a(18)=2, 9=3^2 so a(19)=3, etc...

%Y Cf. A028354, A002828

%K easy,nonn

%O 1,7

%A _Ctibor O. Zizka_, Mar 13 2010