A353295 Square nearest to the sum of the first n positive squares.

0, 1, 4, 16, 25, 49, 100, 144, 196, 289, 400, 484, 625, 841, 1024, 1225, 1521, 1764, 2116, 2500, 2916, 3364, 3844, 4356, 4900, 5476, 6241, 6889, 7744, 8464, 9409, 10404, 11449, 12544, 13689, 14884, 16129, 17689, 19044, 20449, 22201, 23716, 25600, 27556, 29241

Offset

0,3

Links

Paolo Xausa, Table of n, a(n) for n = 0..9999

Formula

a(n) = A053187(A000330(n)).

Example

a(4) = 25 because the sum of the first 4 positive squares is 1 + 4 + 9 + 16 = 30, and the nearest square is 25.

Mathematica

nterms=100; Array[Round[Sqrt[#(#+1)(2#+1)/6]]^2&, nterms, 0]

Prog

(Python)
from math import isqrt
def a(n):
    s = n*(n+1)*(2*n+1)//6
    r = isqrt(s)
    d1, d2 = s-r**2, (r+1)**2-s
    return r**2 if d1 <= d2 else (r+1)**2
print([a(n) for n in range(45)]) # Michael S. Branicky, Jun 05 2022

Crossrefs

Cf. A000290, A000330, A053187, A351830, A354330.

Sequence in context: A135556 A163095 A075576 * A363428 A295921 A338406

Adjacent sequences: A353292 A353293 A353294 * A353296 A353297 A353298

Keyword

nonn,easy

Author

Paolo Xausa, Jun 04 2022

Status

approved