Enigma 1239: The next number…
21 April 2015
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From New Scientist #2395, 17th May 2003 [link]
Joe took a sheet of lined paper and asked me to write a whole number on the first line. This I did, writing a number that was less than a million and which consisted of the same digit repeated several times. After some elaborate calculations Joe wrote a number of the second line. After more calculations he wrote a number on the third line, and he continued like this until he had written a huge number on the eighth line. I asked him how he calculated each number. He explained, “If the number N is on one line then I work out the remainders when N is divided by 5 or 6. In some cases the first remainder was larger than the second and in those cases I wrote the square of N+1 on the next line. In the other cases the first remainder was smaller than the second and I wrote the cube of N+2 on the next line.”
What number did I write on the first line?