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A364143 a(n) is the minimal number of consecutive squares needed to sum to A216446(n).

%I A364143 #27 Aug 08 2023 18:04:30
%S A364143 2,5,3,2,2,3,10,2,7,9,12,11,6,11,14,3,11,29,14,7,23,4,49,8,24,5,17,12,
%T A364143 38,46,27,34,6,14,22,66,11,66,14,11,6,77,36,63,96,11,50,3,19,96,52,41,
%U A364143 66,33,11,3,14,121,66,89,34,127,51,2,86,54,181,48,8
%N A364143 a(n) is the minimal number of consecutive squares needed to sum to A216446(n).
%H A364143 Project Euler, <a href="https://projecteuler.net/problem=125">Problem 125: Palindromic Sums</a>.
%e A364143 a(8) = 7 is because 7 consecutive squares are needed to sum to A216446(8) = 595 = 6^2 + 7^2 + 8^2 + 9^2 + 10^2 + 11^2 + 12^2.
%o A364143 (Python)
%o A364143 is_palindrome = lambda n: str(n) == str(n)[::-1]
%o A364143 def g(L):
%o A364143   L2, squares, D = L*L, [x*x for x in range(0, L + 1)], {}
%o A364143   for i in range(1, L + 1):
%o A364143     for j in range(i + 1, L + 1):
%o A364143       candidate = sum(squares[i:j+1])
%o A364143       if candidate < L2 and is_palindrome(candidate):
%o A364143         if candidate in D:
%o A364143           D[candidate]= min(D[candidate], j-i-1)
%o A364143         else:
%o A364143           D[candidate] = j-i+1
%o A364143   return [D[k] for k in sorted(D.keys())]
%o A364143 print(g(1000))
%Y A364143 Cf. A216446, A034705, A180436, A267600.
%K A364143 nonn,base
%O A364143 1,1
%A A364143 _Darío Clavijo_, Jul 10 2023