A372498 Complement of A372477.

8, 11, 14, 15, 18, 22, 23, 29, 32, 35, 38, 40, 41, 45, 47, 51, 53, 54, 55, 58, 59, 62, 66, 68, 69, 71, 74, 77, 78, 80, 83, 87, 88, 92, 95, 96, 98, 99, 105, 106, 107, 113, 115, 116, 118, 119, 123, 125, 126, 128, 130, 131, 134, 135, 137, 138, 141, 143, 149, 150, 153, 154, 155

Offset: 1

Author

Yury Kazakov, S. P. Obukhov, Sean Sun, and N. A. Shikhova, May 03 2024

Keywords

• nonn

Comments

Sequence is complement of A372477.

This sequence consists of the positive integers that cannot be represented in the form (n*n + k*k - k*n, n*n + k*k - k*n + k - n), n > 0, 0 <= k < n.

Links

• Yury Kazakov, Table of n, a(n) for n = 1..1000
• N. A. Shikhova, Discussion of a problem on the social network VK (in Russian).
• N. A. Shikhova, Illustration for the sequence A372477.

Crossrefs

Complement of A372477.

Programs

Python

import math
L=20 #tr are terms A372477 below L**2+1
numb=set()
Lmax=math.trunc((1+2*math.sqrt(3*L**2+1))/3)+1
tr=set()
tr.add(1)
for n in range(2,Lmax):
  for k in range(0,n):
    p1=n*n+k*k-k*n
    p2=p1+k-n
    if p1<=L**2:
      tr.add(p1)
    if p2<=L**2:
      tr.add(p2)
for k in  range (1, L**2):
  numb.add(k)
print(sorted(numb-tr))