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.

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

Offset: 1

Author

Leroy Quet, Jun 28 2009

Keywords

• base
• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A077459.

Programs

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 *)

Extensions

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