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

%I A049354 #29 Nov 20 2024 08:37:45
%S A049354 11,15,19,21,260,266,268,278,290,294,302,304,308,312,316,318,332,344,
%T A049354 348,380,384,396,410,412,416,420,424,426,434,438,450,460,462,468,500,
%U A049354 502,508,518,520,524,528,532,534,544,550,552,572,574,578,582,586,588,596
%N A049354 Digitally balanced numbers in base 3: equal numbers of 0's, 1's, 2's.
%H A049354 Alois P. Heinz, <a href="/A049354/b049354.txt">Table of n, a(n) for n = 1..2000</a>
%F A049354 A062756(a(n)) = A077267(a(n)) and A081603(a(n)) = A077267(a(n)). - _Reinhard Zumkeller_, Aug 09 2014
%t A049354 Select[Range[600],Length[Union[DigitCount[#,3]]]== 1&]
%t A049354 FromDigits[#,3]&/@DeleteCases[Flatten[Permutations/@Table[PadRight[{},3n,{1,0,2}],{n,3}],1],_?(#[[1]]==0&)]//Sort (* _Harvey P. Dale_, May 30 2016 *)
%t A049354 Select[Range@5000, Differences@DigitCount[#,3]=={0,0}&] (* _Hans Rudolf Widmer_, Dec 11 2021 *)
%o A049354 (Haskell)
%o A049354 a049354 n = a049354_list !! (n-1)
%o A049354 a049354_list = filter f [1..] where
%o A049354    f n = t0 == a062756 n && t0 == a081603 n where t0 = a077267 n
%o A049354 -- _Reinhard Zumkeller_, Aug 09 2014
%o A049354 (Python)
%o A049354 from sympy.ntheory import count_digits
%o A049354 def ok(n): c = count_digits(n, 3); return c[0] == c[1] == c[2]
%o A049354 print([k for k in range(600) if ok(k)]) # _Michael S. Branicky_, Nov 15 2021
%Y A049354 Cf. A031443, A031944.
%Y A049354 Cf. A049354-A049360. See also A061854, A037861.
%Y A049354 Cf. A062756, A077267, A081603.
%Y A049354 Row n = 3 of A378000.
%K A049354 nonn,base
%O A049354 1,1
%A A049354 _Harvey P. Dale_