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

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, 38, 46, 27, 34, 6, 14, 22, 66, 11, 66, 14, 11, 6, 77, 36, 63, 96, 11, 50, 3, 19, 96, 52, 41, 66, 33, 11, 3, 14, 121, 66, 89, 34, 127, 51, 2, 86, 54, 181, 48, 8

Offset: 1

Author

Darío Clavijo, Jul 10 2023

Keywords

• nonn
• base

Examples

			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.
		

Links

• Project Euler, Problem 125: Palindromic Sums.

Crossrefs

Cf. A216446, A034705, A180436, A267600.

Programs

Python

is_palindrome = lambda n: str(n) == str(n)[::-1]
def g(L):
  L2, squares, D = L*L, [x*x for x in range(0, L + 1)], {}
  for i in range(1, L + 1):
    for j in range(i + 1, L + 1):
      candidate = sum(squares[i:j+1])
      if candidate < L2 and is_palindrome(candidate):
        if candidate in D:
          D[candidate]= min(D[candidate], j-i-1)
        else:
          D[candidate] = j-i+1
  return [D[k] for k in sorted(D.keys())]
print(g(1000))