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

1,1

Links

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

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A031443, A143147, A351599.

Sequence in context: A225465 A248665 A066324 * A298663 A325936 A185755

Adjacent sequences: A143143 A143144 A143145 * A143147 A143148 A143149

Keyword

base,nonn

Author

Leroy Quet, Jul 27 2008

Extensions

More terms from Emeric Deutsch, Aug 16 2008

Status

approved