A216446 -id:A216446 - cp's OEIS frontend

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

Darío Clavijo, Jul 10 2023

			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.

Project Euler, Problem 125: Palindromic Sums.

Cf. A216446, A034705, A180436, A267600.

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))

A180436 Palindromic numbers which are sum of consecutive squares.

Original entry on oeis.org

1, 4, 5, 9, 55, 77, 121, 181, 313, 434, 484, 505, 545, 595, 636, 676, 818, 1001, 1111, 1441, 1771, 4334, 6446, 10201, 12321, 14641, 17371, 17871, 19691, 21712, 40804, 41214, 42924, 44444, 44944, 46564, 51015, 65756, 69696, 81818, 94249, 97679, 99199

Offset: 1

Zhining Yang, Jan 19 2011

In more than one way: 554455, 9343439, ... (A267600) - Robert G. Wilson v, May 28 2012

			1001 is in the sequence because 1001 is palindromic and it can be written as sum of consecutive squares (1001 = 4^2 + 5^2 + 6^2 + ... + 13^2 + 14^2).

Giovanni Resta, Table of n, a(n) for n = 1..10400 (terms < 10^18, first 228 terms from Robert G. Wilson v)

Cf. A002113, A002779, A034705, A216446, A267600.

palQ[n_Integer] := Block[{idn = IntegerDigits[n]}, idn == Reverse[idn]]; lst = {}; k = 1; While[k < 1000, AppendTo[lst, Select[ Accumulate[ Range[k, 1000]^2], palQ]]; lst = Union@ Flatten@ lst; k++]; Select[lst, # < 10^6 &] (* Robert G. Wilson v, May 28 2012 *)

cp's OEIS Frontend

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

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