

A162215


a(n) is the smallest multiple of n that is greater than 2n and contains the same number of 1's in its binary representation as n contains.


1



4, 8, 9, 16, 20, 18, 21, 32, 36, 40, 44, 36, 52, 42, 45, 64, 68, 72, 76, 80, 84, 88, 92, 72, 100, 104, 108, 84, 116, 90, 93, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 135, 184, 188, 144, 196, 200, 153, 208, 212, 216, 220, 168, 228, 232, 236
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OFFSET

1,1


COMMENTS

a(n) = 3n only if n is in sequence A077459. Otherwise, a(n) = 4n.


LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000


EXAMPLE

15 in binary is 1111, which contains four 1's as binary digits. 15*3 = 45, which is 101101 in binary. This also contains four 1's. So a(15) = 3*15 = 45.


MAPLE

A000120 := proc(n) add(d, d=convert(n, base, 2)) ; end: A162215 := proc(n) local k; for k from 3 do if A000120(k*n)= A000120(n) then RETURN(k*n) ; fi; od: end: seq(A162215(n), n=1..80) ; # R. J. Mathar, Jul 04 2009


MATHEMATICA

Array[Block[{k = 3, d = DigitCount[#, 2, 1]}, While[DigitCount[k #, 2, 1] != d, k++]; k #] &, 59] (* Michael De Vlieger, Feb 24 2019 *)


CROSSREFS

Cf. A077459.
Sequence in context: A336359 A003679 A079432 * A134344 A324278 A119315
Adjacent sequences: A162212 A162213 A162214 * A162216 A162217 A162218


KEYWORD

base,nonn


AUTHOR

Leroy Quet, Jun 28 2009


EXTENSIONS

a(4) corrected and sequence extended by R. J. Mathar, Jul 04 2009


STATUS

approved



