A366091 -id:A366091 - cp's OEIS frontend

A366064 Record values of A366091.

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, 74, 78, 79, 84, 90, 92, 96, 102, 104, 112, 113, 129, 133, 136, 137, 149, 153, 163, 165, 176, 178, 190, 192, 196, 200, 209, 226, 237, 244, 253, 273, 284, 299, 316, 317, 320, 329, 347, 360, 361, 380, 385

Offset: 1

Robert Israel, Sep 28 2023

nonn

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.

			a(6) = 7 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.

Cf. A366065, A366091.

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)]:
B:= NULL: m:= 0:
for i from 1 to 250001 do
  if L[i] > m then
     m:= L[i]; B:=B,m
  fi
od:
B;

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

A366065 Positions of records in A366091.

Original entry on oeis.org

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

Robert Israel, Sep 28 2023

nonn

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.

			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.

Cf. A366064, A366091.

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;

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

cp's OEIS Frontend

A366064 Record values of A366091.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

Formula