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%I #18 Mar 05 2024 07:10:52
%S 0,2,4,8,10,12,16,18,24,32,34,36,38,40,42,48,52,56,64,66,68,70,80,82,
%T 96,100,112,128,130,132,134,136,138,140,142,144,146,148,150,160,162,
%U 168,170,176,178,192,196,200,204,208,212,224,232,240,256,258,260,262,264
%N 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.
%C All terms of this sequence are even.
%C 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
%C Number of terms < 2^k: 1, 2, 3, 6, 18, 27, 54, 81,... (A038754). - _T. D. Noe_, Apr 09 2009
%H T. D. Noe, <a href="/A140900/b140900.txt">Table of n, a(n) for n=1..1000</a>
%e 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.
%t 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 *)
%o (PARI) is(n) = my (b=if (n, binary(n), [0])); vecmax(b+Vecrev(b))<=1 \\ _Rémy Sigrist_, Jun 11 2022
%Y A035928 is a subsequence.
%K base,nonn
%O 1,2
%A _Leroy Quet_, Jul 24 2008
%E More terms from _Robert G. Wilson v_, Aug 04 2008
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