A383252 Numbers that cannot be written in the form (j+2k)^2-(j+k)^2-j^2 with j,k>0.

1, 2, 5, 6, 8, 9, 10, 13, 14, 17, 18, 21, 22, 24, 25, 26, 29, 30, 33, 34, 37, 38, 40, 41, 42, 45, 46, 49, 50, 53, 54, 56, 57, 58, 61, 62, 65, 66, 69, 70, 72, 73, 74, 77, 78, 81, 82, 85, 86, 88, 89, 90, 93, 94, 97, 98, 101, 102, 104, 105, 106, 109, 110, 113

Offset

1,2

Comments

Numbers congruent to {1, 2, 5, 6, 8, 9, 10, 13, 14} mod 16.

Also, numbers not of the form (j+k)*(3k-j) for j,k>0.

These numbers do not have any pair of divisors x, y such that x+y is a multiple of 4.

Links

Table of n, a(n) for n=1..64.

Project Euler, Problem 135: Same Differences.

Prog

(Python)
isok = lambda n: (n & 15) in [1, 2, 5, 6, 8, 9, 10, 13, 14]
print([n for n in range(1, 256) if isok(n)])

Crossrefs

Cf. A364168.

Sequence in context: A090946 A299417 A047442 * A005781 A157850 A049636

Adjacent sequences: A383249 A383250 A383251 * A383253 A383254 A383255

Keyword

nonn

Author

Darío Clavijo, Apr 20 2025

Status

approved