A366064 - OEIS

%I #9 Sep 29 2023 02:18:32

%S 1,2,3,4,5,7,8,11,15,16,19,21,23,24,25,28,32,33,34,39,48,50,60,64,65,

%T 74,78,79,84,90,92,96,102,104,112,113,129,133,136,137,149,153,163,165,

%U 176,178,190,192,196,200,209,226,237,244,253,273,284,299,316,317,320,329,347,360,361,380,385

%N Record values of A366091.

%C Numbers m such that for some v, there are exactly m ways to write v = i^2 + 2*j^2 + 3*k^2 with i,j,k >= 0, and fewer than m ways to write w = i^2 + 2*j^2 + 3*k^2 for every w < v.

%F a(n) = A366091(A366065(n)).

%e a(6) = 7 is a term because 36 = 6^2 + 2*0^2 + 3*0^2 = 2^2 + 2*4^2 + 3*0^2

%e = 5^2 + 2*2^2 + 3*1^2 = 1^2 + 2*4^2 + 3*1^2 = 4^2 + 2*2^2 + 3*2^2 = 3^2 + 2*0^2 + 3*3^2 = 1^2 + 2*2^2 + 3*3^2 can be written as i^2 + 2*j^2 + 3*k^2 in 7 ways, and all numbers < 36 can be written in fewer than 7 ways.

%p g:= add(z^(i^2),i=0..500) * add(z^(2*i^2),i=0..floor(500/sqrt(2))) *

%p add(z^(3*i^2),i=0..floor(500/sqrt(3))):

%p S:= series(g,z,250001):

%p L:= [seq(coeff(S,z,i),i=0..250000)]:

%p B:= NULL: m:= 0:

%p for i from 1 to 250001 do

%p   if L[i] > m then

%p      m:= L[i]; B:=B,m

%p   fi

%p od:

%p B;

%Y Cf. A366065, A366091.

%K nonn

%O 1,2

%A _Robert Israel_, Sep 28 2023