A281378 Palindromic numbers which are also palindromic in their binary reflected Gray code representation.

0, 1, 2, 5, 6, 66, 77, 626, 5005, 7777, 22122, 64446, 87978, 399993, 1287821, 5614165, 5679765, 6407046, 6865686, 7107017, 8349438, 8547458, 282777282, 1220330221, 43474247434, 43833533834, 64630703646, 68622322686, 73855855837, 1249451549421, 2468208028642

Offset: 1

Author

Indranil Ghosh, Jan 20 2017

Keywords

• nonn
• base

Examples

			626 is in the sequence because binary reflected Gray code for 626 is '1101001011' and both 626 and '1101001011' are palindromics.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..47

Crossrefs

Cf. A002113, A006995, A014550, A281379.

Programs

Mathematica

Select[Range[10^7], And[Reverse@ # == # &@ IntegerDigits@ #, Reverse@ # == # &@ Abs[Prepend[Most@ #, 0] - #] &@ IntegerDigits[#, 2]] &] (* Michael De Vlieger, Jan 21 2017 *)

PARI

lista(nn) = {my(v, w); for(k=0, nn, if((w=digits(k))==Vecrev(w) && (v=binary(bitxor(k, k>>1)))==Vecrev(v), print1(k, ", "))); } \\ Jinyuan Wang, Mar 01 2020

Python

def G(n):
    return bin(n^(n//2))[2:]
i=1
j=1
while j<=23:
    if  i==int(str(i)[::-1]) and G(i)==G(i)[::-1]:
        print(str(j)+" "+str(i))
        j+=1
    i+=1

Extensions

0 and more terms added by Chai Wah Wu, Jan 23 2017