# Dimitroff's Puzzle

N. J. A. Sloane njas at research.att.com
Wed Jun 2 16:21:01 CEST 2004

```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

Would someone please consider all sequences of
the form  "a(n) = N written in base n."
for N up to some reasonable limit,
and submit any sequences that would make good puzzles to the OEIS?

Only those that involve digits between 0 and 9 can appear,
which rules out most of them.

Some of the others may already be in the OEIS

Always give both versions, which tells you when to stop in the
second version (when you hit a nondecimal digit) and hence
where to start in the first sequence.

BTW, there are many variations. For example:

%I A053715
%S A053715 0,1,11,20,22,30,33,40,44,50,55,60,66,70,77,80,88,90,99,100,110,110,
%T A053715 121,120,132,130,143,140,154,150,165,160,176,170,187,180,198,190,209,
%U A053715 200,220,210,231,220,242,230,253,240,264,250,275,260,286,270,297,280
%N A053715 Triangular numbers (the sum of the first n integers) in base n.
%F A053715 Apart from a(1), a(2n-1)=10n and a(2n)=11n
%e A053715 a(3)=1+2+3=6 =20base3
%Y A053715 Cf. A000217.
%K A053715 base,easy,nonn
%O A053715 0,3
%A A053715 Henry Bottomley (se16(AT)btinternet.com), Feb 10 2000
%E A053715 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 22 2000

Thanks

NJAS

```