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

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, 36, 40, 42, 45, 48, 51, 54, 56, 60, 62, 63, 64, 65, 66, 68, 72, 73, 80, 84, 85, 90, 93, 96, 99, 102, 107, 108, 112, 119, 120, 124, 126, 127, 128, 129, 130, 132, 136, 144, 146, 153

Offset: 1

Author

Leroy Quet, Jun 14 2009

Keywords

• base
• nonn

Comments

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.

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

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

Examples

			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.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A030101, A057890, A071687.

Programs

Maple

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

Mathematica

Select[Range@ 153, Divisible[#, FromDigits[Reverse@ IntegerDigits[#, 2], 2]] &] (* Michael De Vlieger, Sep 04 2015 *)

PARI

is(n, base=2) = my (r=fromdigits(Vecrev(digits(n, base)), base)); n%r==0 \\ Rémy Sigrist, Apr 04 2020

Extensions

Extended by R. J. Mathar, Jun 18 2009