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

Author

Paolo Xausa, Jun 04 2022

Keywords

• nonn
• easy

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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

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

Formula

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