A158930 - OEIS

%I #8 Jun 25 2018 03:47:09

%S 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,

%T 27,24,28,62,29,63,30,64,31,52,33,54,41,60,34,53,46,65,49,67,45,68,

%U 100,32,75,36,78,37,79,56,90,39,93,35,94,51,98,55,99,57,95,61,103,156,69

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

%C 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,...

%H Robert Israel, <a href="/A158930/b158930.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%p for S in combinat:-powerset({$0..4}) minus {{},{$0..4}} do

%p   if member(0,S) then Last[S]:= 0 else Last[S]:= 1 fi od:

%p Next:= proc(S)

%p   global Last; local L, nL;

%p   if nops(S) = 1 then Last[S]:= Last[S]*5+S[1]; return Last[S] fi;

%p   Last[S]:= 1+Last[S];

%p   L:= convert(Last[S],base,nops(S));

%p   nL:= nops(L);

%p   if (not member(0,S)) then

%p    if L[-1] > 1 then

%p     Last[S]:= (nops(S))^nL;

%p     L:= [0$nL,1];

%p    else nL:= nL-1

%p    fi

%p   fi;

%p   L:= subs({seq(i-1=S[i],i=1..nops(S))},L);

%p   add(L[i]*5^(i-1),i=1..nL)

%p end proc:

%p Done:= {1}:

%p A[1]:= 1:

%p for n from 2 to 100 do

%p   S:= {$0..4} minus convert(convert(A[n-1],base,5),set);

%p   do

%p     x:= Next(S);

%p     if not member(x,Done) then break fi

%p   od;

%p   A[n]:= x;

%p   Done:= Done union {x};

%p od:

%p seq(A[i],i=1..100); # _Robert Israel_, Jun 25 2018

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

%K base,easy,nonn,look

%O 1,2

%A _R. J. Mathar_, Mar 31 2009