A302058 Numbers that are not square pyramidal numbers.

2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82

Offset

1,1

Comments

Numbers not of the form 0^2 + 1^2 + 2^2 + ... + m^2 = m*(m + 1)*(2*m + 1)/6.

Links

Table of n, a(n) for n=1..77.

Eric Weisstein's World of Mathematics, Square Pyramidal Number

Formula

a(n) = n+m if 6n>m(m-1)(2m+5) and a(n) = n+m-1 otherwise where m = floor((3n)^(1/3)). - Chai Wah Wu, Oct 01 2024

Mathematica

Module[{nn=6, m}, m=(nn(nn+1)(2nn+1))/6 ; Complement[Range[m], Table[(n(n+1)(2n+1))/6, {n, nn}]]] (* Harvey P. Dale, Aug 22 2020 *)

Prog

(Python)
from sympy import integer_nthroot
def A302058(n): return n+(m:=integer_nthroot(3*n, 3)[0])-(6*n<=m*(m-1)*(2*m+5)) # Chai Wah Wu, Oct 01 2024

Crossrefs

Complement of A000330.

Cf. A000037, A014132, A145397, A253903.

Sequence in context: A230313 A052413 A276389 * A183302 A323733 A003247

Adjacent sequences: A302055 A302056 A302057 * A302059 A302060 A302061

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Mar 31 2018

Status

approved