A342873 Numbers whose distance to the nearest cube equals the distance to the nearest product of 3 consecutive integers (three-dimensional oblong).

0, 7, 16, 62, 92, 213, 276, 508, 616, 995, 1160, 1722, 1956, 2737, 3052, 4088, 4496, 5823, 6336, 7990, 8620, 10637, 11396, 13812, 14712, 17563, 18616, 21938, 23156, 26985, 28380, 32752, 34336, 39287, 41072, 46638, 48636, 54853, 57076, 63980, 66440, 74067

Offset: 1

Author

Lamine Ngom, Mar 28 2021

Keywords

• nonn
• easy

Comments

That is, numbers k such that A074989(k) = A342872(k).

They form 2 partitions:

7, 62, 213, ... = 8*k^3 - k = k*A157914(k).

0, 16, 92, ... = 8*k^3 + 6*k^2 + 2*k = 2*k*A033951(k).

Crossrefs

Cf. A074989, A342872.

Cf. A157914, A033951, A074378, A201053, A000578, A007531, A081134.

Programs

Python

def aupto(limit):
  cubes = [k**3 for k in range(int((limit+1)**1/3)+2)]
  proms = [k*(k+1)*(k+2) for k in range(int((limit+1)**1/3)+1)]
  A074989 = [min(abs(n-c) for c in cubes) for n in range(limit+1)]
  A342872 = [min(abs(n-p) for p in proms) for n in range(limit+1)]
  return [m for m in range(limit+1) if A074989[m] == A342872[m]]
print(aupto(10**4)) # Michael S. Branicky, Mar 28 2021