A031946 -id:A031946 - cp's OEIS frontend

A049356 Digitally balanced numbers in base 5: equal numbers of 0's, 1's, ..., 4's.

694, 698, 714, 722, 738, 742, 894, 898, 954, 970, 978, 990, 1014, 1022, 1054, 1070, 1102, 1110, 1138, 1142, 1178, 1190, 1202, 1210, 1294, 1298, 1334, 1346, 1358, 1366, 1394, 1398, 1454, 1470, 1478, 1490, 1634, 1646, 1654, 1670, 1726, 1730, 1758, 1766, 1778

Offset: 1

Harvey P. Dale

The first 96 (=4*4!) terms of this sequence and of A031946 are identical. a(97) = 1001223344_5 = 1976724.

			a(1) = 10234_5 = 694.
a(96) = 43210_5 = 2930.

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 96 terms from Vincenzo Librandi)

Cf. A031443.
Subsequence of A031946.
Row n = 5 of A378000.

Select[Range[5000], Length[Union[DigitCount[#, 5]]]==1&] (* Vincenzo Librandi, Apr 18 2013 *)

Edited by Rick L. Shepherd, Jun 22 2003

A158930 a(n) is the smallest integer not yet in the sequence with no common base-5 digit with a(n-1).

Original entry on oeis.org

1, 2, 3, 4, 5, 12, 6, 10, 8, 14, 15, 7, 18, 9, 13, 20, 11, 19, 25, 17, 21, 50, 16, 22, 26, 23, 27, 24, 28, 62, 29, 63, 30, 64, 31, 52, 33, 54, 41, 60, 34, 53, 46, 65, 49, 67, 45, 68, 100, 32, 75, 36, 78, 37, 79, 56, 90, 39, 93, 35, 94, 51, 98, 55, 99, 57, 95, 61, 103, 156, 69

Offset: 1

R. J. Mathar, Mar 31 2009

Numbers of A031946 or of the 4th row of A051845 do not appear in this sequence. In base-5 notation the sequence reads 1,2,3,4,10,22,11,20,13,24,30,12,33,14,...

			The terms a(1) to a(4) are the first integers in order because they have only a single, non-common digit. a(5)=5(base10)=10(base5) does not share a digit with a(4)=4(base10)=4(base5). The numbers 6(base10)=11(base5) to 9(base10)=14(base5) are ruled out for a(6) because they share a 1 with 10(base5). The numbers 10(base10)=20(base5) and 11(base10)=21(base5) are also ruled out for a(6) because they either have a 0 or a 1 in common with a(5)=10(base5). So a(6)=12(base10)=22(base5) with no 0 or 1 is selected.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A067581 (base-10), A158928 (base-3), A158929 (base-4).

for S in combinat:-powerset({$0..4}) minus {{},{$0..4}} do
  if member(0,S) then Last[S]:= 0 else Last[S]:= 1 fi od:
Next:= proc(S)
  global Last; local L, nL;
  if nops(S) = 1 then Last[S]:= Last[S]*5+S[1]; return Last[S] fi;
  Last[S]:= 1+Last[S];
  L:= convert(Last[S],base,nops(S));
  nL:= nops(L);
  if (not member(0,S)) then
   if L[-1] > 1 then
    Last[S]:= (nops(S))^nL;
    L:= [0$nL,1];
   else nL:= nL-1
   fi
  fi;
  L:= subs({seq(i-1=S[i],i=1..nops(S))},L);
  add(L[i]*5^(i-1),i=1..nL)
end proc:
Done:= {1}:
A[1]:= 1:
for n from 2 to 100 do
  S:= {$0..4} minus convert(convert(A[n-1],base,5),set);
  do
    x:= Next(S);
    if not member(x,Done) then break fi
  od;
  A[n]:= x;
  Done:= Done union {x};
od:
seq(A[i],i=1..100); # Robert Israel, Jun 25 2018

cp's OEIS Frontend

A049356 Digitally balanced numbers in base 5: equal numbers of 0's, 1's, ..., 4's.

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