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

%I A281382 #22 Nov 22 2024 15:07:21
%S A281382 2,3,5,6,13,70,213,217,229,253,422,426,446,465,534,541,705,741,857,
%T A281382 869,8441,8481,9190,9221,9293,10210,10349,10453,10929,11049,12006,
%U A281382 12281,12329,12721,12793,14109,14282,20578,20934,21009,21629,21701,22810,22866,23221,23421,28705,29397
%N A281382 Numbers n such that the decimal equivalent of the binary reflected Gray code representation of n is a palindromic prime.
%C A281382 Numbers n such that A003188(n) is both prime and palindromic.
%H A281382  Indranil Ghosh and Chai Wah Wu, <a href="/A281382/b281382.txt">Table of n, a(n) for n = 1..13824</a>, first 1281 terms from Indranil Ghosh.
%e A281382 213 is in the sequence because A003188(213) = 191 and 191 is a palindromic prime.
%t A281382 Select[Range@ 30000, And[PrimeQ@ #, Reverse@ # == # &@ IntegerDigits@ #] &@ BitXor[#, Floor[#/2]] &] (* _Michael De Vlieger_, Mar 30 2017 *)
%o A281382 (Python)
%o A281382 from sympy import isprime
%o A281382 def G(n):
%o A281382     return int(bin(n^(n//2))[2:],2)
%o A281382 i=0
%o A281382 j=1
%o A281382 while j<=1281:
%o A281382     if G(i)==int(str(G(i))[::-1]) and isprime(G(i))==True:
%o A281382         print(j, i)
%o A281382         j+=1
%o A281382     i+=1
%Y A281382 Cf. A002385, A003188.
%K A281382 nonn,base
%O A281382 1,1
%A A281382 _Indranil Ghosh_, Jan 21 2017