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A353295 Square nearest to the sum of the first n positive squares. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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
Sequence in context: A135556 A163095 A075576 * A363428 A295921 A338406
KEYWORD
nonn,easy
AUTHOR
Paolo Xausa, Jun 04 2022
STATUS
approved

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Last modified April 17 13:58 EDT 2024. Contains 371764 sequences. (Running on oeis4.)