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

%I A353295 #29 Jul 15 2022 11:28:54
%S A353295 0,1,4,16,25,49,100,144,196,289,400,484,625,841,1024,1225,1521,1764,
%T A353295 2116,2500,2916,3364,3844,4356,4900,5476,6241,6889,7744,8464,9409,
%U A353295 10404,11449,12544,13689,14884,16129,17689,19044,20449,22201,23716,25600,27556,29241
%N A353295 Square nearest to the sum of the first n positive squares.
%H A353295 Paolo Xausa, <a href="/A353295/b353295.txt">Table of n, a(n) for n = 0..9999</a>
%F A353295 a(n) = A053187(A000330(n)).
%e A353295 a(4) = 25 because the sum of the first 4 positive squares is 1 + 4 + 9 + 16 = 30, and the nearest square is 25.
%t A353295 nterms=100;Array[Round[Sqrt[#(#+1)(2#+1)/6]]^2&,nterms,0]
%o A353295 (Python)
%o A353295 from math import isqrt
%o A353295 def a(n):
%o A353295     s = n*(n+1)*(2*n+1)//6
%o A353295     r = isqrt(s)
%o A353295     d1, d2 = s-r**2, (r+1)**2-s
%o A353295     return r**2 if d1 <= d2 else (r+1)**2
%o A353295 print([a(n) for n in range(45)]) # _Michael S. Branicky_, Jun 05 2022
%Y A353295 Cf. A000290, A000330, A053187, A351830, A354330.
%K A353295 nonn,easy
%O A353295 0,3
%A A353295 _Paolo Xausa_, Jun 04 2022