[ *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 = 4635__666__5364_{{7}}

9458132760 = B79__666__97B_{{13}}

The indiscriminate beast, present in lucky base 7 as in unlucky base 13 !

1068274359 = 99__666__99_{{22}}

1980467253 = HA__666__AH_{{22}}

2183675904 = EH__666__HE_{{23}}

2956037184 = JM__666__MJ_{{23}}

6240573918 = K5__666__5K_{{26}}

The beast hides in other places as well.

The following is my favourite one

495328176 = 234__666__432_{{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 = 11__MOM__11_{{31}}

7851423096 = D5__MOM__5D_{{29}}

5846103279 = 3Q__MOM__Q3_{{34}}

Tribute to my parents. But where are my DAD's ?

Oh, here they are ! More DAD's than MOM's ?

6731289450 = 47B__DAD__B74_{{14}}

8467509312 = 13A__DAD__A31_{{17}}

1724385609 = 90__DAD__09_{{24}}

9421368570 = 54__DAD__45_{{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