

A158930


a(n) is the smallest integer not yet in the sequence with no common base5 digit with a(n1).


3



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
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OFFSET

1,2


COMMENTS

Numbers of A031946 or of the 4th row of A051845 do not appear in this sequence. In base5 notation the sequence reads 1,2,3,4,10,22,11,20,13,24,30,12,33,14,...


LINKS



EXAMPLE

The terms a(1) to a(4) are the first integers in order because they have only a single, noncommon 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:= nL1
fi
fi;
L:= subs({seq(i1=S[i], i=1..nops(S))}, L);
add(L[i]*5^(i1), i=1..nL)
end proc:
Done:= {1}:
A[1]:= 1:
for n from 2 to 100 do
S:= {$0..4} minus convert(convert(A[n1], base, 5), set);
do
x:= Next(S);
if not member(x, Done) then break fi
od;
A[n]:= x;
Done:= Done union {x};
od:


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



