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A049357 Digitally balanced numbers in base 6: equal numbers of 0's, 1's, ..., 5's.

%I A049357 #21 Nov 20 2024 08:38:17
%S A049357 8345,8350,8375,8385,8410,8415,8525,8530,8585,8600,8620,8630,8735,
%T A049357 8745,8765,8780,8835,8840,8950,8955,8980,8990,9015,9020,10505,10510,
%U A049357 10535,10545,10570,10575,11045,11050,11165,11190,11200,11220,11255
%N A049357 Digitally balanced numbers in base 6: equal numbers of 0's, 1's, ..., 5's.
%C A049357 Subset of A031947. [_R. J. Mathar_, Oct 15 2008]
%H A049357 Vincenzo Librandi, <a href="/A049357/b049357.txt">Table of n, a(n) for n = 1..600</a>
%e A049357 8345 is 102345 in base 6.
%p A049357 isA049357 := proc(n)
%p A049357     local ct60, ct61,ct62,ct63,ct64,ct65,d ;
%p A049357     ct60 := 0 ; ct61 := 0 ; ct62 := 0 ;
%p A049357     ct63 := 0 ; ct64 := 0 ; ct65 := 0 ;
%p A049357     for d in convert(n,base,6) do
%p A049357         if d = 0 then
%p A049357             ct60 := ct60+1 ;
%p A049357         elif d = 1 then
%p A049357             ct61 := ct61+1 ;
%p A049357         elif d =2 then
%p A049357             ct62 := ct62+1 ;
%p A049357         elif d =3 then
%p A049357             ct63 := ct63+1 ;
%p A049357         elif d =4 then
%p A049357             ct64 := ct64+1 ;
%p A049357         elif d =5 then
%p A049357             ct65 := ct65+1 ;
%p A049357         end if ;
%p A049357     end do:
%p A049357     if ct60 = ct61 and ct61 = ct62 and ct62 = ct63 and ct63 = ct64 and ct64 = ct65 then
%p A049357         return true ;
%p A049357     else
%p A049357         return false;
%p A049357     end if;
%p A049357 end proc:
%p A049357 for n from 1 to 12000 do
%p A049357     if isA04957(n) then
%p A049357         print(n);
%p A049357     end if;
%p A049357 end do: # _R. J. Mathar_, Aug 24 2023
%t A049357 Select[Range[6000], Length[Union[DigitCount[#, 6]]] == 1 &] (* _Vincenzo Librandi_, Apr 18 2013 *)
%Y A049357 Cf. A031443.
%Y A049357 Row n = 6 of A378000.
%K A049357 nonn,base
%O A049357 1,1
%A A049357 _Harvey P. Dale_