A140900 A nonnegative integer n is included if the binary representation of n and the digit-reversal (with leading 0's) of the binary representation of n do not have any 1's in the same position.

0, 2, 4, 8, 10, 12, 16, 18, 24, 32, 34, 36, 38, 40, 42, 48, 52, 56, 64, 66, 68, 70, 80, 82, 96, 100, 112, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 160, 162, 168, 170, 176, 178, 192, 196, 200, 204, 208, 212, 224, 232, 240, 256, 258, 260, 262, 264

Offset: 1

Author

Leroy Quet, Jul 24 2008

Keywords

• base
• nonn

Comments

All terms of this sequence are even.

Number of terms less than or equal to 10^n: 1, 5, 26, 162, 1045, 5976, 38980, 249229, 1416583, 9381238, ..., . - Robert G. Wilson v, Aug 04 2008

Number of terms < 2^k: 1, 2, 3, 6, 18, 27, 54, 81,... (A038754). - T. D. Noe, Apr 09 2009

Examples

			36 in binary is 100100. The digit-reversal (with leading 0's) of this is 001001. These binary representations have no 1's in the same location (i.e., they can be added in binary without any carries). So 36 is in this sequence.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Crossrefs

A035928 is a subsequence.

Programs

Mathematica

fQ[n_] := Block[{id = IntegerDigits[n, 2]}, Max@ Union[id + Reverse@ id] < 2]; Select[2 Range[0, 134], fQ@# &] (* Robert G. Wilson v, Aug 04 2008 *)

PARI

is(n) = my (b=if (n, binary(n), [0])); vecmax(b+Vecrev(b))<=1 \\ Rémy Sigrist, Jun 11 2022

Extensions

More terms from Robert G. Wilson v, Aug 04 2008