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

1,2

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

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A030101, A057890, A071687.

Sequence in context: A062014 A164707 A057890 * A125121 A333762 A295235

Adjacent sequences: A161601 A161602 A161603 * A161605 A161606 A161607

Keyword

base,nonn

Author

Leroy Quet, Jun 14 2009

Extensions

Extended by R. J. Mathar, Jun 18 2009

Status

approved