[ November 6, 2001 ]
Exploring Nine- & Pandigitals in other bases... your turn

This is a package that barely got freed from its wrapping paper.
I hope it will become fully exposed but for that to happen I very
much need your contributions. What I am particularly interested in
are Nine- & Pandigital numbers with noteworthy properties
or curiosities when converted in other base systems. As for
myself I am a little bit hooked up to palindromes so my examples
will come from that angle but that is absolutely not a requirement !

9518234076 = 1DOGGOD1_{25}
A mystical revelation. Is there only 1 god ?

9510284673 = 106666666601_{8}
The binary bounded expanded beast ! Note the 8 sixes.

1394257806 = 46356665364_{7}
9458132760 = B7966697B_{13}
The indiscriminate beast, present in lucky base 7 as in unlucky base 13 !

1068274359 = 9966699_{22}
1980467253 = HA666AH_{22}
2183675904 = EH666HE_{23}
2956037184 = JM666MJ_{23}
6240573918 = K56665K_{26}
The beast hides in other places as well.

The following is my favourite one
495328176 = 234666432_{11}
Note that the sum of the two sidenumbers
234 + 432 equals the beastly middle part 666 and
495 + 328 + 176 is 999 or the beast upside down !

351872469 = 99A11A99_{12}
The only ninedigital that is palindromic in base 12.

937186452 = 11MOM11_{31}
7851423096 = D5MOM5D_{29}
5846103279 = 3QMOMQ3_{34}
Tribute to my parents. But where are my DAD's ?

Oh, here they are ! More DAD's than MOM's ?
6731289450 = 47BDADB74_{14}
8467509312 = 13ADADA31_{17}
1724385609 = 90DAD09_{24}
9421368570 = 54DAD45_{35}

143287569 = 1000100010100110010100010001_{2}
1058674239 = 111111000110100001011000111111_{2}
The smallest nine- & pandigitals that are base 2 palindromic.
What are the largest solutions ?

What is wrong with bases {3} and {9} ?

I didn't find any nine- or pandigitals that are palindromic
when converted into these bases 3 or 9.
Exist there a numbertheoretical proof ?

Extra reading material from
A. Bogomolny, Number System With Base 36