cp's OEIS Frontend

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

%I A161604 #23 Apr 04 2020 15:10:23
%S A161604 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 A161604 36,40,42,45,48,51,54,56,60,62,63,64,65,66,68,72,73,80,84,85,90,93,96,
%U A161604 99,102,107,108,112,119,120,124,126,127,128,129,130,132,136,144,146,153
%N A161604 A positive integer k is included if the value of (the reversal of k's representation in binary) divides k.
%C A161604 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 A161604 It seems (verified for the first 120000 entries) that a(n) = A057890(n+1). - _R. J. Mathar_, Jun 18 2009
%C A161604 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
%H A161604 Rémy Sigrist, <a href="/A161604/b161604.txt">Table of n, a(n) for n = 1..10000</a>
%e A161604 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 A161604 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 A161604 Select[Range@ 153, Divisible[#, FromDigits[Reverse@ IntegerDigits[#, 2], 2]] &] (* _Michael De Vlieger_, Sep 04 2015 *)
%o A161604 (PARI) is(n, base=2) = my (r=fromdigits(Vecrev(digits(n, base)), base)); n%r==0 \\ _Rémy Sigrist_, Apr 04 2020
%Y A161604 Cf. A030101, A057890, A071687.
%K A161604 base,nonn
%O A161604 1,2
%A A161604 _Leroy Quet_, Jun 14 2009
%E A161604 Extended by _R. J. Mathar_, Jun 18 2009