A377721 Numbers that are not of the form k(k+1)(2k+1)/6 + k.

1, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72

Offset: 1

Author

Chai Wah Wu, Nov 04 2024

Keywords

• nonn

Comments

Complement of A145066. Numbers that are not of the form A000330(k)+k.

Crossrefs

Cf. A000330, A074279, A145066.

Programs

Python

from sympy import integer_nthroot
def A377721(n): return n+(m:=integer_nthroot(3*n,3)[0])-(6*n<=m*(m+1)*((m<<1)+1))

Formula

a(n) = n+m if n > m(m+1)(2m+1)/6 and a(n) = n+m-1 otherwise where m = floor((3n)^(1/3)).

a(n) = A074279(n)+n-1.