A049354 Digitally balanced numbers in base 3: equal numbers of 0's, 1's, 2's.

11, 15, 19, 21, 260, 266, 268, 278, 290, 294, 302, 304, 308, 312, 316, 318, 332, 344, 348, 380, 384, 396, 410, 412, 416, 420, 424, 426, 434, 438, 450, 460, 462, 468, 500, 502, 508, 518, 520, 524, 528, 532, 534, 544, 550, 552, 572, 574, 578, 582, 586, 588, 596

Offset: 1

Author

Harvey P. Dale

Keywords

• nonn
• base

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A031443, A031944.

Cf. A049354-A049360. See also A061854, A037861.

Cf. A062756, A077267, A081603.

Row n = 3 of A378000.

Programs

Haskell

a049354 n = a049354_list !! (n-1)
a049354_list = filter f [1..] where
   f n = t0 == a062756 n && t0 == a081603 n where t0 = a077267 n
-- Reinhard Zumkeller, Aug 09 2014

Mathematica

Select[Range[600],Length[Union[DigitCount[#,3]]]== 1&]
FromDigits[#,3]&/@DeleteCases[Flatten[Permutations/@Table[PadRight[{},3n,{1,0,2}],{n,3}],1],?(#[[1]]==0&)]//Sort (* _Harvey P. Dale, May 30 2016 *)
Select[Range@5000, Differences@DigitCount[#,3]=={0,0}&] (* Hans Rudolf Widmer, Dec 11 2021 *)

Python

from sympy.ntheory import count_digits
def ok(n): c = count_digits(n, 3); return c[0] == c[1] == c[2]
print([k for k in range(600) if ok(k)]) # Michael S. Branicky, Nov 15 2021

Formula

A062756(a(n)) = A077267(a(n)) and A081603(a(n)) = A077267(a(n)). - Reinhard Zumkeller, Aug 09 2014