A366065 Positions of records in A366091.

0, 3, 9, 12, 30, 36, 81, 84, 156, 228, 246, 324, 396, 444, 516, 534, 606, 774, 804, 876, 1164, 1614, 1884, 2046, 2244, 2676, 3564, 3684, 3756, 4134, 4404, 4764, 5124, 5646, 6636, 6654, 6924, 7716, 8166, 8724, 9804, 10686, 11334, 12324, 12846, 13476, 15654, 17004, 17796, 18804, 20406, 20694, 21036

Offset

1,2

Comments

Numbers that can be written in the form i^2 + 2*j^2 + 3*k^2 with i,j,k >= 0 in more ways than any previous number.

Links

Table of n, a(n) for n=1..53.

Formula

A366091(a(n)) = A366064(n).

Example

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

Maple

g:= add(z^(i^2), i=0..500) * add(z^(2*i^2), i=0..floor(500/sqrt(2))) *
add(z^(3*i^2), i=0..floor(500/sqrt(3))):
S:= series(g, z, 250001):
L:= [seq(coeff(S, z, i), i=0..250000)]:
A:= NULL: m:= 0:
for i from 1 to 250001 do
  if L[i] > m then
     m:= L[i]; A:=A, i-1
  fi
od:
A;

Crossrefs

Cf. A366064, A366091.

Sequence in context: A081601 A244018 A261950 * A137344 A029524 A357726

Adjacent sequences: A366062 A366063 A366064 * A366066 A366067 A366068

Keyword

nonn

Author

Robert Israel, Sep 28 2023

Status

approved