A263620 Number of nonzero palindromic squares with at most 2n digits.

3, 6, 14, 19, 30, 36, 55, 69, 94, 112, 161, 192, 263, 309, 414, 485, 639, 740, 949, 1081, 1373, 1555

Offset: 1

Author

N. J. A. Sloane, Oct 23 2015

Keywords

• nonn
• base
• more

Links

• G. J. Simmons, Palindromic powers, J. Rec. Math., 3 (No. 2, 1970), 93-98. [Annotated scanned copy] See page 95.

Crossrefs

Cf. A002778, A002779, A263617, A263617, A263618, A263619.

Programs

Mathematica

Table[Length[Select[Range[1, Floor[Sqrt[10^(2 n)]]], PalindromeQ[#^2] &]], {n, 6}] (* Robert Price, Apr 26 2019 *)

Python

def ispal(n): s = str(n); return s == s[::-1]
def a(n):
  c, k, kk = 0, 1, 1
  while kk < 10**(2*n): c, k, kk = c + (ispal(kk)), k+1, kk + 2*k + 1
  return c
print([a(n) for n in range(1, 8)]) # Michael S. Branicky, Mar 06 2021

Formula

Equals A263619(2n)-1.

Extensions

a(7)-a(10) from Chai Wah Wu, Oct 25 2015

More terms using A263618 from Chai Wah Wu, Jun 14 2024