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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. 2
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 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
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
Sequence in context: A062014 A164707 A057890 * A125121 A333762 A295235
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 28 18:11 EST 2024. Contains 370400 sequences. (Running on oeis4.)