Problems & Puzzles: Puzzles

Puzzle 246.  The worms

101232121 is a prime p such that:

  • abs(Di Di+1)=1, for each 1<=i<L; Di is any digit of p
  • ∑(Di-Di+1)=0, where the sum is for i=1 to L-1 (or, if you prefer a simpler statement D1=DL)
  • L is the quantity of digits of p.



a)      The earliest pandigital prime p of this kind

b)      The earliest titanic pandigital prime p of this kind


J. K. Andersen and Jon Wharf got the solution to both questions:

a) 7654321012345678987

b) (10^978-1)/99*10^24+12123456789876543210121 = (10^1002-1)/99+2022446688866442200020 = 1010101......01012123456789876543210121

Faride Firoozbakht also found a).



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