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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 (list; graph; refs; listen; history; text; internal format)
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 *)

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

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Last modified March 7 10:30 EST 2021. Contains 341869 sequences. (Running on oeis4.)