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A253631
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Palindromic primes containing only the digits 0 and 1 such that their squares are palindromes.
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1
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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)
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OFFSET
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1,1
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COMMENTS
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Subsequence of A100580.
Conjecture: a(n) = A225603(n+2).
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LINKS
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Chai Wah Wu, Table of n, a(n) for n = 1..938
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EXAMPLE
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11 is a palindromic prime, and 11^2 = 121 is a palindrome.
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MATHEMATICA
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Select[FromDigits/@Tuples[{0, 1}, 20], PalindromeQ[#]&&PrimeQ[#] && PalindromeQ[ #^2]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 13 2017 *)
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PROG
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(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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CROSSREFS
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Sequence in context: A247863 A180280 A100580 * A087744 A054421 A037700
Adjacent sequences: A253628 A253629 A253630 * A253632 A253633 A253634
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KEYWORD
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nonn,base
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AUTHOR
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Chai Wah Wu, Jan 06 2015
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STATUS
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approved
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