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

1,1

Comments

Subsequence of A100580.

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

Links

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

Example

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

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 *)

Prog

(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)

Crossrefs

Sequence in context: A247863 A180280 A100580 * A087744 A054421 A037700

Adjacent sequences: A253628 A253629 A253630 * A253632 A253633 A253634

Keyword

nonn,base

Author

Chai Wah Wu, Jan 06 2015

Status

approved