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Base-10 puzzle

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  • djbroadhurst
    Find a joual-speaking author who may be googled by supplying the next prime of this sequence: 31, 19, 23, 139, 6089, 40949, 13153513, 748105003 ... Hint: The
    Message 1 of 6 , Jan 16, 2014
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      Find a joual-speaking author who may be googled
      by supplying the next prime of this sequence:
      31, 19, 23, 139, 6089, 40949, 13153513, 748105003 ...

      Hint: The n'th prime in the sequence is the first of a
      sequence of n+1 primes obtained by a base-10 procedure.

      Comment: If you answer with the name of the author,
      you will be unlikely to spoil the puzzle for others.  

      David
    • djbroadhurst
      ... As shrewdly observed by Maximilian Hasler, http://oeis.org/search?q=139+6089+40949 provides a strong clue. David
      Message 2 of 6 , Jan 18, 2014
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        ---In primenumbers@yahoogroups.com, <david.broadhurst@...> wrote:


        > Find a joual-speaking author who may be googled
        > by supplying the next prime of this sequence:
        > 31, 19, 23, 139, 6089, 40949, 13153513, 748105003 ...

        > Hint: The n'th prime in the sequence is the first of a
        > sequence of n+1 primes obtained by a base-10 procedure.

        As shrewdly observed by Maximilian Hasler,
        http://oeis.org/search?q=139+6089+40949
        provides a strong clue.

        David
      • Kevin Acres
        Hi David, Thanks for passing on Maximilian s observation. This was a sufficient enough clue to enable completion the puzzle in a very short time. My answer was
        Message 3 of 6 , Jan 18, 2014
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          Hi David,

          Thanks for passing on Maximilian's observation. This was a sufficient enough clue to enable completion the puzzle in a very short time.

          My answer was sent to you off list.

          Best Regards,

          Kevin.


          At 01:09 AM 19/01/2014, david.broadhurst@... wrote:


          ---In primenumbers@yahoogroups.com, <david.broadhurst@...> wrote:

          > Find a joual-speaking author who may be googled
          > by supplying the next prime of this sequence:
          > 31, 19, 23, 139, 6089, 40949, 13153513, 748105003 ...

          > Hint: The n'th prime in the sequence is the first of a
          > sequence of n+1 primes obtained by a base-10 procedure.

          As shrewdly observed by Maximilian Hasler,
          http://oeis.org/search?q=139+6089+40949
          provides a strong clue.

          David


        • djbroadhurst
          ... I think that Kevin s correct answer, namely that the author is Michel Tremblay, will not spoil the mathematical puzzle. David ... As shrewdly observed by
          Message 4 of 6 , Jan 18, 2014
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            Kevin Acres wrote:


            > Thanks for passing on Maximilian's observation. This was a sufficient
            > enough clue to enable completion of the puzzle in a very short
            time.

            I think that Kevin's correct answer, namely that the author 
            is Michel Tremblay, will not spoil the mathematical puzzle.

            David


            ---In primenumbers@yahoogroups.com, <david.broadhurst@...> wrote:

            > Find a joual-speaking author who may be googled
            > by supplying the next prime of this sequence:
            > 31, 19, 23, 139, 6089, 40949, 13153513, 748105003 ...

            > Hint: The n'th prime in the sequence is the first of a
            > sequence of n+1 primes obtained by a base-10 procedure.

            As shrewdly observed by Maximilian Hasler,
            http://oeis.org/search?q=139+6089+40949
            provides a strong clue.

            David


          • marku606
            ... I think that Kevin s correct answer, namely that the author is Michel Tremblay, will not spoil the mathematical puzzle. David I gave it a go. Discovering
            Message 5 of 6 , Jan 20, 2014
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              ---In primenumbers@yahoogroups.com, <david.broadhurst@...> wrote:

              Kevin Acres wrote:


              > Thanks for passing on Maximilian's observation. This was a sufficient
              > enough clue to enable completion of the puzzle in a very short
              time.

              I think that Kevin's correct answer, namely that the author 
              is Michel Tremblay, will not spoil the mathematical puzzle.

              David

              I gave it a go.  Discovering the 'base-10 procedure' was the easy part, but my computer protested finding the next value in the sequence.  Finally it found the number, ending in 4673.  Funny coincidence that 
              3, 73, 673 and 4673 are all primes.  And of course that is fodder for yet another prime puzzle :) 

              Mark  



              ---In primenumbers@yahoogroups.com, <david.broadhurst@...> wrote:

              > Find a joual-speaking author who may be googled
              > by supplying the next prime of this sequence:
              > 31, 19, 23, 139, 6089, 40949, 13153513, 748105003 ...

              > Hint: The n'th prime in the sequence is the first of a
              > sequence of n+1 primes obtained by a base-10 procedure.

              As shrewdly observed by Maximilian Hasler,
              http://oeis.org/search?q=139+6089+40949
              provides a strong clue.

              David


            • djbroadhurst
              ... The first 10 members of the sequence are 31, 19, 23, 139, 6089, 40949, 13153513, 748105003, 11307204673, 202073177599 a[n] is the smallest prime that
              Message 6 of 6 , Feb 1, 2014
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                Mark Underwood wrote:


                > I gave it a go.  Discovering the 'base-10 procedure' was the easy part,
                > but my computer protested finding the next value in the sequence. 
                > Finally it found the number, ending in 4673.

                Well done. Mark. Here is the solution, with an extra term:

                > Find a joual-speaking author who may be googled
                > by supplying the next prime of this sequence:
                > 31, 19, 23, 139, 6089, 40949, 13153513, 748105003 ...

                > Hint: The n'th prime in the sequence is the first of a
                > sequence of n+1 primes obtained by a base-10 procedure.

                The first 10 members of the sequence are

                31, 19, 23, 139, 6089, 40949, 13153513, 748105003, 11307204673, 202073177599

                a[n] is the smallest prime that remains prime for precisely
                n times when its final decimal digit is repeated.

                Examples:

                a[9] =
                11307204673 is prime, so are
                113072046733,
                1130720467333,
                11307204673333,
                113072046733333,
                1130720467333333,
                11307204673333333,
                113072046733333333,
                1130720467333333333,
                11307204673333333333, but
                113072046733333333333 is composite.
                No prime smaller than 11307204673 has this
                property of precisely 9 prime repetitions.

                a[10] = 202073177599
                print(isprime(vector(13,k,2020731776*10^k-1)))
                [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]

                Googling 11307204673, we obtain
                http://www.abebooks.com/Premier-quartier-lune-Michel-Tremblay-LEM%C3%83/11307204673/bd
                leading us to
                http://fr.wikipedia.org/wiki/Michel_Tremblay
                > Il intègrera le dialecte québécois "joual" dans ses pièces

                David
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