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 More Consecutive Semiprimes (Posted on 2009-09-08)
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 No Rating

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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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