numbersequence
 

Can you figure out the next number in this 'trivial' sequence?

10, 11, 12, 13, 14, 15, 16, 17, 20, 22, 24, 31, 100, 121, ?

-michael

[spoiler]10000[/spoiler]

[spoiler]base 16, base 15, base 14, ... next in sequence is base 2[/spoiler]

[url]http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A008713[/url]

number sequence
 

[QUOTE=michael]Can you figure out the next number in this 'trivial' sequence?

10, 11, 12, 13, 14, 15, 16, 17, 20, 22, 24, 31, 100, 121, ?

-michael[/QUOTE]
Dear Michael,
please explain Dweiks solution.
Mally :yucky:

[QUOTE=mfgoode]Dear Michael,
please explain Dweiks solution.
Mally :yucky:[/QUOTE]
It's the value (1+1+1+1)^(1+1) expressed in radices descending to
the value (1+1+1) and you have to express the final value in the radix (1+1).

How about that for a radix-independent answer?


Paul

(10)[sub]hexadecimal[/sub]=(11)[sub]15[/sub]=(12)[sub]14[/sub]=(13)[sub]13[/sub]=(14)[sub]12[/sub]=(15)[sub]11[/sub]=16[sub]decimal[/sub]=(17)[sub]9[/sub]=(20)[sub]octal[/sub]=(22)[sub]7[/sub]=(24)[sub]6[/sub]=(31)[sub]5[/sub]=(100)[sub]4[/sub]=(121)[sub]3[/sub]=(10000)[sub]binary[/sub]

General:
(abcde)[sub]n[/sub]=(a*n[sup]4[/sup]+b*n[sup]3[/sup]+c*n[sup]2[/sup]+d*n[sup]1[/sup]+e*n[sup]0[/sup])[sub]decimal[/sub]

Hope this answers your question Mally,

-michael

Number Sequence
 

[QUOTE=xilman]It's the value (1+1+1+1)^(1+1) expressed in radices descending to
the value (1+1+1) and you have to express the final value in the radix (1+1).

How about that for a radix-independent answer?


Paul[/QUOTE]
:yucky: Thanks Paul. I still will have to put pen to paper and fathom it out.
Mally.

Number Sequence
 

[QUOTE=michael](10)[sub]hexadecimal[/sub]=(11)[sub]15[/sub]=(12)[sub]14[/sub]=(13)[sub]13[/sub]=(14)[sub]12[/sub]=(15)[sub]11[/sub]=16[sub]decimal[/sub]=(17)[sub]9[/sub]=(20)[sub]octal[/sub]=(22)[sub]7[/sub]=(24)[sub]6[/sub]=(31)[sub]5[/sub]=(100)[sub]4[/sub]=(121)[sub]3[/sub]=(10000)[sub]binary[/sub]

General:
(abcde)[sub]n[/sub]=(a*n[sup]4[/sup]+b*n[sup]3[/sup]+c*n[sup]2[/sup]+d*n[sup]1[/sup]+e*n[sup]0[/sup])[sub]decimal[/sub]

Hope this answers your question Mally,

-michael[/QUOTE]

Number Sequence.
 

Thanks Michael.Still I need a more elementary clarfication.
Mally

Take for instance (14)[sub]12[/sub]=([B]1[/B]*12[sup]1[/sup]+[B]4[/B]*12[sup]0[/sup])[sub]decimal[/sub]=12+4=16

or (121)[sub]3[/sub]=([B]1[/B]*3[sup]2[/sup]+[B]2[/B]*3[sup]1[/sup]+[B]1[/B]*3[sup]0[/sup])[sub]decimal[/sub]=9+6+1=16

other way round: 16=[B]1[/B]*2[sup]4[/sup]+[B]0[/B]*2[sup]3[/sup]+[B]0[/B]*2[sup]2[/sup]+[B]0[/B]*2[sup]1[/sup]+[B]0[/B]*2[sup]0[/sup] so 16=(10000)[sub]2[/sub] or binary

-michael