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 10 Sequences (Posted on 2004-04-23)
Fill in the blanks. All the sequences below follow the same pattern.

1.) 0
2.) 1, 1, 1, 1, 1, 1, 1, 1...
3.) 2, 2, 2, 2, 2, 2, 2, 2...
4.) 5, 5, 5, 5, 5, 5, 5, 5...
5.) 4, 8, 64, 2097152 ...
6.) 6, 36, 10077696 ...
7.) 7, 7, 7, 7, 7, 7, 7, 7...
8.) 9, 27, 729, 14348907 ...
9.) 10, 100, ____, ....
10.) 11, ____ ....

 No Solution Yet Submitted by Victor Zapana Rating: 3.5556 (9 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: got it | Comment 5 of 9 |
(In reply to got it by jesse)

Another way of looking at this is that each successive number is the product of all the divisors of the preceding number, including that number itself (so you don't multiply that number by the product of the factors--it's just the product of the factor (divisors)--including the number itself).

A UBASIC program produces (when a number extends to the edge, it's continued on the next line--that's not a new number):

` 2  2  2  2  2  2  2`
` 3  3  3  3  3  3  3`
` 4  8  64  2097152  3450873173395281893717377931138512726225554486085193277581262111899648`
` 5  5  5  5  5  5  5`
` 6  36  10077696  147252498583517385317586164069238032896112058351438757983014769693372565232993881469948991217709137019461037145294592020173701375168912282334484871403174767655880386045910084758703074415025299415269171925628511937032731984012897986591707883502506548247671311183326452554217858802386703514003611399224036192306226210075368787167671873479497761345765376`
` 7  7  7  7  7  7  7`
` 8  64  2097152  3450873173395281893717377931138512726225554486085193277581262111899648`
` 9  27  729  10460353203  164062694609488086547539746812648575659318856476507740436897453222447961474036515706307096943652603236842951947`
` 10  100  1000000000  1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000`
` 11  11  11  11  11  11  11`
` 12  1728  2116471057875484488839167999221661362284396544`
` 13  13  13  13  13  13  13`
` 14  196  20661046784  572289865518550906473459269984096192380710993219229673657946521844239453332541224966515620411589583479098968189549653903535722666645738483077406698708512390746014952885452052190769204922624980360120525478094952193551831514437559329125870814555210239068034820923267231914992058547700416695831022231250057234728231933312398976102606595406719922406069627083826295043319676805719187215686359718857729436209078923547739998994716544437909110922549417695942189257678736286644499109840378341193998665600647757288557433061376`

where 9  27  729  10460353203  is the only discrepancy from the original puzzle; again, perhaps an error on the part of the poser.

It then confirms that 100 if followed by 1000000000 and 11 is followed by 11.

The program is:

`    5   goto 1000   10   *FactorIt   20         N=abs(Num):if N>0 then Limit=sqrt(N):else Limit=0   22         PSubscr=0   30         if Limit<>int(Limit) then Limit=int(Limit+1)   40         Dv=2:gosub *DivideIt   50         Dv=3:gosub *DivideIt   60         Dv=5:gosub *DivideIt   70         Dv=7   80         while 1   90           gosub *DivideIt:Dv=Dv+4 '11  100          gosub *DivideIt:Dv=Dv+2 '13  110          gosub *DivideIt:Dv=Dv+4 '17  120          gosub *DivideIt:Dv=Dv+2 '19  130          gosub *DivideIt:Dv=Dv+4 '23  140          gosub *DivideIt:Dv=Dv+6 '29  150          gosub *DivideIt:Dv=Dv+2 '31  160          gosub *DivideIt:Dv=Dv+6 '37  170          if inkey=chr(27) then S\$=chr(27):goto *Finis  171          if Dv>Limit then goto *Outloop  180         wend  188       *Outloop  190        if N>1 then  191           :if N=PDivsr(PSubscr) then NOccur(PSubscr)=NOccur(PSubscr)+1:else PSubscr=PSubscr+1:PDivsr(PSubscr)=N:NOccur(PSubscr)=1:endif  200    return`
`  220       *DivideIt  230       while 1  240         Q=int(N/Dv)  250         if Q*Dv=N and N>0 then  260           :N=Q:if N>0 then Limit=sqrt(N):else Limit=0:endif  262           :if Dv=PDivsr(PSubscr) then NOccur(PSubscr)=NOccur(PSubscr)+1:else PSubscr=PSubscr+1:PDivsr(PSubscr)=Dv:NOccur(PSubscr)=1:endif  270           :if Limit<>int(Limit) then Limit=int(Limit+1):else nop:endif  280         :else  290          :return  300        :endif  310       wend  320        return`
` 1000   dim PDivsr(30) 1010   dim NOccur(30):dim NTms(30) 1020   for NStart=2 to 14 1030     Num=NStart:print Num; 1035     Iter=1 1036     while Iter<=6 1040      erase PDivsr():erase NOccur() 1050      dim PDivsr(30):dim NOccur(30) 1060      gosub *FactorIt 1070      T=1:if PSubscr>0 then gosub *Analyze(1) 1075      print T;:if T>10^20 then Iter=9 1080      Num=T:Iter=Iter+1 1190     wend 1195   print:print 1200   next NStart 1300   end`
` 2000   *Analyze(S) 2010   local NumTimes,I,J,Noc 2090   Noc=NOccur(S) 2100   for NumTimes=0 to Noc 2110      NTms(S)=NumTimes 2120      if S=PSubscr then 2140        :for I=1 to PSubscr 2150        :for J=1 to NTms(I) 2160        :T=T*PDivsr(I) 2170        :next J 2180        :next I 2190      :else 2200        :gosub *Analyze(S+1) 2215   next NumTimes 2390   return`

Edited on April 26, 2004, 3:42 pm
 Posted by Charlie on 2004-04-26 15:40:42

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