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
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
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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)
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