Dimitroff's Puzzle
Pfoertner, Hugo
Hugo.Pfoertner at muc.mtu.de
Thu Jun 3 09:38:24 CEST 2004
Neil, SeqFans,
[ note after having written the first part of the message: The actual
content of A094203 and A094232 exactly reflects my suggestion that was based
on the versions included in Neils original seqfan message reproduced at
bottom of message ]
--- start of obsolete part ----
although it's tempting to include the 111....111 term in
http://www.research.att.com/projects/OEIS?Anum=A094203 and
http://www.research.att.com/projects/OEIS?Anum=A094232
(my opinion would be to move it to the comment), there should be at least a
remark similar to the one given in
http://www.research.att.com/projects/OEIS?Anum=A065147
saying that the only number representible in base 1 is "0".
---- end of obsolete part ----
I never worried about that (personally I find most of the base-related
sequences uninteresting), but the present discussion led me to "invent"
http://www.research.att.com/projects/OEIS?Anum=A095026
1,
3,1,
5,2,2,
8,2,4,2,
9,4,4,4,4,
15,2,6,5,6,2,
13,6,6,6,6,6,6,
20,4,8,4,12,4,8,4,
21,6,6,12,6,6,12,6,6,
27,4,12,4,12,9,12,4,12,4,
... could probably be extended ...
21,......
Lower triangle T(j,k) read by rows, where T(j,k) is the number of
occurrences of the digit k-1 as least significant digit in the base-j
multiplication table. The only reasonable choice for T(1,1)=a(1) is 1 - see
http://www.research.att.com/projects/OEIS?Anum=A018804
which is identical to the first column of A095026.
Hugo
-----Ursprüngliche Nachricht-----
Von: N. J. A. Sloane [mailto:njas at research.att.com]
Gesendet am: Mittwoch, 2. Juni 2004 16:21
An: Pfoertner, Hugo; Antti Karttunen
Cc: seqfan at ext.jussieu.fr
Betreff: Re: Dimitroff's Puzzle
Fermat's valet would have thought that one was ancient.
Still, I added it, in two versions:
%I A094203
%S A094203 20,22,24,26,30,33,40,44,120,220,11000,111111111111111111111111
%N A094203 a(n) = 24 written in base 13-n.
%D A094203 Marilyn vos Savant, "Ask Marilyn," in 'Parade', Sunday, Apr 26
1999.
%O A094203 1,1
%K A094203 nonn,base
%Y A094203 Cf. A094232, A065147, etc.
%A A094203 njas, Jun 02 2004
%I A094232
%S A094232 111111111111111111111111,11000,220,120,44,40,33,30,26,24,22,20
%N A094232 a(n) = 24 written in base n.
%C A094232 The next term involves a non-decimal number.
%D A094232 Marilyn vos Savant, "Ask Marilyn," in 'Parade', Sunday, Apr 26
1999.
%O A094232 1,1
%K A094232 nonn,base
%Y A094232 Cf. A094203, A065147, etc.
%A A094232 njas, Jun 02 2004
[ snip ]
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