login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A302058
Numbers that are not square pyramidal numbers.
4
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
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.
Sequence in context: A230313 A052413 A276389 * A183302 A323733 A003247
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Mar 31 2018
STATUS
approved