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A253631
Palindromic primes containing only the digits 0 and 1 such that their squares are palindromes.
1
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
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
KEYWORD
nonn,base,changed
AUTHOR
Chai Wah Wu, Jan 06 2015
STATUS
approved