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

1,3

Links

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

Example

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

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A002113, A006995, A014550, A281379.

Sequence in context: A365503 A055877 A288799 * A219117 A111190 A244434

Adjacent sequences: A281375 A281376 A281377 * A281379 A281380 A281381

Keyword

nonn,base

Author

Indranil Ghosh, Jan 20 2017

Extensions

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

Status

approved