cp's OEIS Frontend

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

%I A253631 #17 Nov 06 2024 15:27:17
%S A253631 11,101,100111001,110111011,111010111,1100011100011,1100101010011,
%T A253631 1101010101011,100110101011001,101000010000101,101011000110101,
%U A253631 101110000011101,10000010101000001,10011010001011001,10100110001100101,10110010001001101,10111000000011101,11010001010001011,1000010101010100001,1001010100010101001
%N A253631 Palindromic primes containing only the digits 0 and 1 such that their squares are palindromes.
%C A253631 Subsequence of A100580.
%C A253631 Conjecture: a(n) = A225603(n+2).
%H A253631 Chai Wah Wu, <a href="/A253631/b253631.txt">Table of n, a(n) for n = 1..938</a>
%e A253631 11 is a palindromic prime, and 11^2 = 121 is a palindrome.
%t A253631 Select[FromDigits/@Tuples[{0,1},20],PalindromeQ[#]&&PrimeQ[#] && PalindromeQ[ #^2]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Feb 13 2017 *)
%t A253631 Select[FromDigits/@Tuples[{0,1},20],PrimeQ[#]&&AllTrue[{#,#^2},PalindromeQ]&] (* _Harvey P. Dale_, Jan 14 2024 *)
%o A253631 (Python)
%o A253631 from sympy import isprime
%o A253631 A253631_list = [11]
%o A253631 for i in range(2, 2**30):
%o A253631     s = format(i, 'b')
%o A253631     x = int(s+s[-2::-1])
%o A253631     s2 = str(x*x)
%o A253631     if s2 == s2[::-1] and isprime(x):
%o A253631         A253631_list.append(x)
%K A253631 nonn,base
%O A253631 1,1
%A A253631 _Chai Wah Wu_, Jan 06 2015