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A161604 A positive integer n is included if the value of (the reversal of n's representation in binary) divides n. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

By "reversal" of n's representation in binary, it is meant: write n in binary (without its leading 0's) from most significant digits on the right and least significant digits on the left, instead of writing n from left to right as is usual. Then interpret the new integer by reading it from left to right.

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

Table of n, a(n) for n=1..67.

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 *)

CROSSREFS

Cf. A030101, A057890, A071687.

Sequence in context: A062014 A164707 A057890 * A125121 A295235 A136490

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

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Last modified February 16 19:44 EST 2019. Contains 320167 sequences. (Running on oeis4.)