A143146 a(n) is the smallest positive multiple of n that has the same number of 0's as 1's in its binary representation.

2, 2, 9, 12, 10, 12, 35, 56, 9, 10, 44, 12, 52, 42, 135, 240, 153, 180, 38, 180, 42, 44, 184, 216, 50, 52, 135, 56, 232, 150, 527, 992, 165, 170, 35, 180, 37, 38, 156, 240, 41, 42, 172, 44, 135, 184, 141, 240, 49, 50, 153, 52, 212, 216, 165, 56, 228, 232, 177, 180

Offset: 1

Author

Leroy Quet, Jul 27 2008

Keywords

• base
• nonn

Examples

			For n = 7, checking: 7*1 = 7 = 111_2; 7*2 = 14 = 1110_2; 7*3 = 21 = 10101_2; 7*4 = 28 = 11100_2. All of these have two many 1's in binary. But 7*5 = 35 = 100011_2, which has both three 0's and three 1's. So a(7) = 35.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A031443, A143147, A351599.

Programs

Maple

a:=proc(n) local b,k: b:=proc(m) convert(m,base,2) end proc: for k while add(b(k*n)[j],j=1..nops(b(k*n))) <> nops(b(k*n))-add(b(k*n)[j],j=1..nops(b(k*n))) do end do: k*n end proc: seq(a(n),n=1..60); # Emeric Deutsch, Aug 16 2008

Mathematica

spm[n_]:=Module[{k=1},While[DigitCount[k*n,2,0]!=DigitCount[k*n,2,1], k++]; k*n]; Array[spm,60] (* Harvey P. Dale, Apr 25 2014 *)

Python

def a(n):
    m = n
    b = bin(m)[2:]
    while len(b) != 2*b.count("1"):
        m += n
        b = bin(m)[2:]
    return m
print([a(n) for n in range(1, 61)]) # Michael S. Branicky, May 15 2022

Formula

a(n) = n * A351599(n). - Rémy Sigrist, Jul 11 2022

Extensions

More terms from Emeric Deutsch, Aug 16 2008