[seqfan] Re: A098786 incorrect
Richard Mathar
mathar at strw.leidenuniv.nl
Mon Mar 30 16:35:24 CEST 2009
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
More information about the SeqFan
mailing list