A253631 Palindromic primes containing only the digits 0 and 1 such that their squares are palindromes.

11, 101, 100111001, 110111011, 111010111, 1100011100011, 1100101010011, 1101010101011, 100110101011001, 101000010000101, 101011000110101, 101110000011101, 10000010101000001, 10011010001011001, 10100110001100101, 10110010001001101, 10111000000011101, 11010001010001011, 1000010101010100001, 1001010100010101001

Offset: 1

Author

Chai Wah Wu, Jan 06 2015

Keywords

• nonn
• base

Comments

Subsequence of A100580.

Conjecture: a(n) = A225603(n+2).

Examples

			11 is a palindromic prime, and 11^2 = 121 is a palindrome.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..938

Programs

Mathematica

Select[FromDigits/@Tuples[{0,1},20],PalindromeQ[#]&&PrimeQ[#] && PalindromeQ[ #^2]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 13 2017 *)
Select[FromDigits/@Tuples[{0,1},20],PrimeQ[#]&&AllTrue[{#,#^2},PalindromeQ]&] (* Harvey P. Dale, Jan 14 2024 *)

Python

from sympy import isprime
A253631_list = [11]
for i in range(2, 2**30):
    s = format(i, 'b')
    x = int(s+s[-2::-1])
    s2 = str(x*x)
    if s2 == s2[::-1] and isprime(x):
        A253631_list.append(x)