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More Consecutive Semiprimes (Posted on 2009-09-08) Difficulty: 3 of 5
Consider the series of semiprimes. Now consider the series of numbers representing the Sum Of Digits (SOD) of each semiprime.

(1.) How many times does the number '9' occur, and why?

(2.) What is the smallest semiprime that has the same SOD as the next consecutive semiprime? or prove that there is no pair of consecutive semiprimes that have the same SOD.

No Solution Yet Submitted by Larry    
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re: part 2 (computer solution) UBASIC version Comment 4 of 4 |
(In reply to part 2 (computer solution) by Daniel)

list
   10   for I=1 to 7000
   20   if fnSemiPrime(I) then
   25   :if fnSod(I)=Prv then print PrvNo,
   30   :print I,fnSod(I):endif:PrvNo=I:Prv=fnSod(I)
   50   next
  200   end
  300
  400   fnSemiPrime(X)
  410   if prmdiv(X)=X then return(0)
  420   N=X//prmdiv(X)
  430   if prmdiv(N)=N then return(-1)
  440   return(0)
  500   fnSod(X)
  505   local T,I
  510   Xstr=cutspc(str(X))
  520   T=0
  530   for I=1 to len(Xstr):T=T+val(mid(Xstr,I,1)):next
  540   return(T)
OK

 

 semiprimes     SOD
 146     155     11
 226     235     10
 278     287     17
 346     355     13
 1018    1027    10
 1177    1186    16
 1273    1282    13
 1546    1555    16
 1865    1874    20
 1945    1954    19
 2138    2147    14
 2545    2554    16
 2762    2771    17
 2869    2878    25
 3118    3127    13
 3317    3326    14
 3817    3826    19
 4022    4031    8
 4045    4054    13
 4069    4078    19
 4126    4135    13
 4213    4222    10
 4249    4258    19
 4322    4331    11
 4417    4426    16
 4502    4511    11
 4918    4927    22
 5114    5123    11
 5389    5398    25
 5438    5447    20
 5473    5482    19
 5515    5533    16
 5645    5663    20
 5677    5686    25
 5855    5873    23
 6169    6178    22
 6209    6218    17
 6218    6227    17
 6362    6371    17
 6649    6658    25
 6826    6835    22

  Posted by Charlie on 2009-09-08 23:58:21
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