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 A161604 A positive integer k is included if the value of (the reversal of k's representation in binary) divides k. 0

%I

%S 1,2,3,4,5,6,7,8,9,10,12,14,15,16,17,18,20,21,24,27,28,30,31,32,33,34,

%T 36,40,42,45,48,51,54,56,60,62,63,64,65,66,68,72,73,80,84,85,90,93,96,

%U 99,102,107,108,112,119,120,124,126,127,128,129,130,132,136,144,146,153

%N A positive integer k is included if the value of (the reversal of k's representation in binary) divides k.

%C By "reversal" of k's representation in binary, it is meant: write k in binary, reverse the order of its digits, and read the result as a binary value.

%C It seems (verified for the first 120000 entries) that a(n) = A057890(n+1). - _R. J. Mathar_, Jun 18 2009

%C Indeed, this is A057890 (palindromes with optional trailing zeros) without the initial term. In other bases this does not have to be so, as illustrated by A071687. - _Ivan Neretin_, Sep 04 2015

%e 24 in binary is 11000. The reversal of this is 11 (ignoring leading 0's), which is 3 in decimal. Since 3 divides 24, then 24 is included in this sequence.

%p A030101 := proc(n) local bdgs ; bdgs := convert(n,base,2) ; add( op(-i,bdgs)*2^(i-1),i=1..nops(bdgs)) ; end: isA161604 := proc(n) if ( n mod A030101(n) ) = 0 then true ; else false; fi; end: for n from 1 to 600 do if isA161604(n) then printf("%d,",n) ; fi; od: # _R. J. Mathar_, Jun 18 2009

%t Select[Range@ 153, Divisible[#, FromDigits[Reverse@ IntegerDigits[#, 2], 2]] &] (* _Michael De Vlieger_, Sep 04 2015 *)

%Y Cf. A030101, A057890, A071687.

%K base,nonn

%O 1,2

%A _Leroy Quet_, Jun 14 2009

%E Extended by _R. J. Mathar_, Jun 18 2009

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Last modified March 26 16:33 EDT 2019. Contains 321510 sequences. (Running on oeis4.)