OFFSET
1,2
COMMENTS
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
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.
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
CROSSREFS
KEYWORD
AUTHOR
R. J. Mathar, Mar 31 2009
STATUS
approved