A034822 Numbers k such that there are no palindromic squares of length k.

2, 4, 8, 10, 14, 18, 20, 24, 30, 38, 40

Offset: 1

Author

Patrick De Geest, Oct 15 1998

Keywords

• nonn
• base
• hard
• more

Comments

All terms are even since (10^k+1)^2 is a palindrome of length 2*k+1. a(12) >= 46 if it exists (see A263618). - Chai Wah Wu, Jun 14 2024

Links

• Patrick De Geest, Palindromic Squares in bases 2 to 17
• Eric Weisstein's World of Mathematics, Palindromic Number

Crossrefs

Cf. A002778, A002779, A034307, A263618.

Programs

Mathematica

A034822[n_] := Select[Range[Ceiling[Sqrt[10^(n - 1)]], Floor[Sqrt[10^n]]], #^2 == IntegerReverse[#^2] &];
Select[Range[12], Length[A034822[#]] == 0 &] (* Robert Price, Apr 23 2019 *)

Python

from sympy import integer_nthroot as iroot
def ispal(n): s = str(n); return s == s[::-1]
def ok(n):
  for r in range(iroot(10**(n-1), 2)[0] + 1, iroot(10**n, 2)[0]):
    if ispal(r*r): return False
  return True
print([m for m in range(1, 16) if ok(m)]) # Michael S. Branicky, Feb 04 2021

Extensions

Two more terms from Patrick De Geest, Apr 01 2002