[seqfan] Re: A098786 incorrect

[Richard Mathar]

dw> From seqfan-bounces at list.seqfan.eu Mon Mar 30 16:03:17 2009
dw> Date: Mon, 30 Mar 2009 09:51:06 -0400
dw> From: David Wilson <dwilson at gambitcomm.com>
dw> To: Sequence Fanatics <seqfan at list.seqfan.eu>
dw> Subject: [seqfan]  A098786 incorrect
dw> 
dw> A098786 is an incorrect version of A067581.

Indeed. Should the corresponding base-3, base-4 and base-5
sequences be put into the OEIS?

 [1, 2, 3, 8, 4, 6, 13, 18, 40, 20, 121, 24, 364, 26, 9, 80, 10, 242, 12, 728]

    [1, 2, 3, 4, 10, 5, 8, 7, 32, 13, 34, 15, 6, 12, 9, 48, 21, 11, 16, 14]

    [1, 2, 3, 4, 5, 12, 6, 10, 8, 14, 15, 7, 18, 9, 13, 20, 11, 19, 25, 17]

I leave the answer to the question "why is the base-2 case left out?" as an exercise
to the interested reader :-(

The philosophical question is: if the base-dependent sequences are
made explicit by putting them into the database for a bunch of different
bases, does that make them less offending to common taste (less base-dependent,
that is) ?

# true if no common digit of x and y in base b
nocomm := proc(x,y,b)
        if convert(convert(x,base,b) ,set) intersect convert(convert(y,base,b) , set) = {} then
                true ;
        else
                false;
        fi;
end:

# Return list as in A098786 for base b
a067 := proc(b)
        local L,a ;
        L := [1] ;
        while nops(L) < 20 do
                for a from 1 do
                        if not a in L then
                                if nocomm(a,op(-1,L),b) then
                                        L := [op(L),a] ;
                                        break ;
                                fi;
                        fi;
                od:
        od:
end:
a067(3) ; # base 3
a067(4) ; # base 4
a067(5) ; # base 5