numbersequence

michael · 2004-01-14, 06:32

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

cheesehead · 2004-01-14, 16:51

10000

dweick · 2004-01-19, 18:29

base 16, base 15, base 14, ... next in sequence is base 2

GP2 · 2004-01-20, 03:48

http://www.research.att.com/cgi-bin/...i?Anum=A008713

mfgoode · 2004-01-25, 11:19

Quote:

Originally Posted by 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

Dear Michael,
please explain Dweiks solution.
Mally

xilman · 2004-01-25, 13:05

Quote:

Originally Posted by mfgoode

Dear Michael,
please explain Dweiks solution.
Mally

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

michael · 2004-01-25, 14:53

(10)_hexadecimal=(11)₁₅=(12)₁₄=(13)₁₃=(14)₁₂=(15)₁₁=16_decimal=(17)₉=(20)_octal=(22)₇=(24)₆=(31)₅=(100)₄=(121)₃=(10000)_binary

General:
(abcde)_n=(a*n⁴+b*n³+c*n²+d*n¹+e*n⁰)_decimal

Hope this answers your question Mally,

-michael

mfgoode · 2004-01-25, 16:23

Quote:

Originally Posted by 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

Thanks Paul. I still will have to put pen to paper and fathom it out.
Mally.

mfgoode · 2004-01-25, 16:25

Quote:

Originally Posted by michael

(10)_hexadecimal=(11)₁₅=(12)₁₄=(13)₁₃=(14)₁₂=(15)₁₁=16_decimal=(17)₉=(20)_octal=(22)₇=(24)₆=(31)₅=(100)₄=(121)₃=(10000)_binary

General:
(abcde)_n=(a*n⁴+b*n³+c*n²+d*n¹+e*n⁰)_decimal

Hope this answers your question Mally,

-michael

mfgoode · 2004-01-25, 16:30

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

michael · 2004-01-25, 16:40

Take for instance (14)₁₂=(1*12¹+4*12⁰)_decimal=12+4=16

or (121)₃=(1*3²+2*3¹+1*3⁰)_decimal=9+6+1=16

other way round: 16=1*2⁴+0*2³+0*2²+0*2¹+0*2⁰ so 16=(10000)₂ or binary

-michael

2004-01-14, 06:32	#1
michael Dec 2003 Belgium 1000001₂ Posts	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

2004-01-25, 16:30	#10
mfgoode Bronze Medalist Jan 2004 Mumbai,India 2²·3³·19 Posts	Number Sequence. Thanks Michael.Still I need a more elementary clarfication. Mally

2004-01-14, 16:51	#2
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 2²×3×641 Posts	10000

2004-01-19, 18:29	#3
dweick Apr 2003 12₈ Posts	base 16, base 15, base 14, ... next in sequence is base 2

2004-01-20, 03:48	#4
GP2 Sep 2003 5031₈ Posts	http://www.research.att.com/cgi-bin/...i?Anum=A008713

2004-01-25, 14:53	#7
michael Dec 2003 Belgium 41₁₆ Posts	(10)_hexadecimal=(11)₁₅=(12)₁₄=(13)₁₃=(14)₁₂=(15)₁₁=16_decimal=(17)₉=(20)_octal=(22)₇=(24)₆=(31)₅=(100)₄=(121)₃=(10000)_binary General: (abcde)_n=(an⁴+bn³+cn²+dn¹+e*n⁰)_decimal Hope this answers your question Mally, -michael

2004-01-25, 16:40	#11
michael Dec 2003 Belgium 5·13 Posts	Take for instance (14)₁₂=(112¹+412⁰)_decimal=12+4=16 or (121)₃=(13²+23¹+13⁰)_decimal=9+6+1=16 other way round: 16=12⁴+02³+02²+02¹+02⁰ so 16=(10000)₂ or binary -michael