A078839 Numbers k such that the binary expansion of 3^k has the same number of 0's and 1's.

2, 12, 69, 73, 150, 184, 252, 328, 339, 464, 483, 541, 729, 747, 758, 763, 1014, 1047, 1090, 1094, 1158, 1264, 1359, 1601, 1679, 1693, 1698, 1780, 2368, 2641, 2815, 3292, 3393, 3606, 3682, 3857, 3909, 3919, 3963, 4087, 4111, 4289, 4314, 5017, 5398, 5466

Offset

1,1

Comments

Does the limit of a(n)/n^2 as n -> infinity exist?

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..1600 (terms 1..1000 from Amiram Eldar)

Amiram Eldar, Plot of a(n)/n^2 for n = 1..1000

Hugo Pfoertner, Plot of a(n)/n^2 using Plot 2.

Mathematica

balanced[n_] := Module[{d=IntegerDigits[n, 2]}, Plus@@d==Length[d]/2]; Select[Range[0, 5500], balanced[3^# ]&]

Prog

(PARI) is(n)=hammingweight(n=3^n)==hammingweight(bitneg(n, #binary(n))) \\ Charles R Greathouse IV, Mar 29 2013

Crossrefs

Cf. A000244, A004656, A011754, A031443.

Sequence in context: A359489 A329789 A245854 * A243771 A026306 A116398

Adjacent sequences: A078836 A078837 A078838 * A078840 A078841 A078842

Keyword

nonn,base

Author

Benoit Cloitre, Dec 06 2002

Status

approved