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Smallest pandifibo number (Posted on 2017-04-29) Difficulty: 3 of 5
What is the smallest zeroless pandigital number in Fibonacci series?

Bonus: find the next smallest zeroless "pandifibo" number.

No Solution Yet Submitted by Ady TZIDON    
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Solution UBASIC solution Comment 1 of 1
   n         F(n)
 125   59425114757512643212875125 
 184   127127879743834334146972278486287885163 
 
 from
 
    4   kill "pandfibo.txt":open "pandfibo.txt" for output as #2
    5   A=1:B=1:Lvl=2
   10   while C<9999999999999999999999999999999999999999
   20     C=A+B:A=B:B=C:inc Lvl
   30     S$=str(C)
   50     Good=1
   60     for I=1 to 9
   70        if instr(S$,cutspc(str(I)))=0 then Good=0:cancel for:goto 90
   80     next
   90     if Good then
   91       :if instr(S$,"0")=0 then print C:Ct=Ct+1:print #2,Lvl,C
  100   wend
  110   print Ct:close #2

The 3-digit numbers preceding the F numbers are the ordinal position of these Fibonacci numbers, in the system where F(1)=F(2)=1.

No further results come from even over 200 9's in line 10. The probability of avoiding any zeros is probably too low with increased numbers of digits. In fact even if C is allowed to go up to 10^999, no further examples are found. There could be a hypothesis that there are no further examples beyond these two (proof anyone), or a probability that no further examples exist, based on an infinite series of probabilities for the infinite series of Fibonacci's that increase in length at a regular rate.

  Posted by Charlie on 2017-04-29 13:57:59
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