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

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

Author

R. J. Mathar, Mar 31 2009

Keywords

• base
• easy
• nonn
• look

Comments

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,...

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Maple

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