A281382 Numbers n such that the decimal equivalent of the binary reflected Gray code representation of n is a palindromic prime.

2, 3, 5, 6, 13, 70, 213, 217, 229, 253, 422, 426, 446, 465, 534, 541, 705, 741, 857, 869, 8441, 8481, 9190, 9221, 9293, 10210, 10349, 10453, 10929, 11049, 12006, 12281, 12329, 12721, 12793, 14109, 14282, 20578, 20934, 21009, 21629, 21701, 22810, 22866, 23221, 23421, 28705, 29397

Offset: 1

Author

Indranil Ghosh, Jan 21 2017

Keywords

• nonn
• base

Comments

Numbers n such that A003188(n) is both prime and palindromic.

Examples

			213 is in the sequence because A003188(213) = 191 and 191 is a palindromic prime.
		

Links

• Indranil Ghosh and Chai Wah Wu, Table of n, a(n) for n = 1..13824, first 1281 terms from Indranil Ghosh.

Crossrefs

Cf. A002385, A003188.

Programs

Mathematica

Select[Range@ 30000, And[PrimeQ@ #, Reverse@ # == # &@ IntegerDigits@ #] &@ BitXor[#, Floor[#/2]] &] (* Michael De Vlieger, Mar 30 2017 *)

Python

from sympy import isprime
def G(n):
    return int(bin(n^(n//2))[2:],2)
i=0
j=1
while j<=1281:
    if G(i)==int(str(G(i))[::-1]) and isprime(G(i))==True:
        print(j, i)
        j+=1
    i+=1