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Given the number sequence

0,1,4,9,0,1,9,1,4,2,1,3,0,4,1,5,4,6,9,7,0,9,9,a,4,?,?,?,?,?,?

the challenge is to

  1. Determine the value represented by a
  2. Predict the next 6 entries represented by ?

Note that

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    $\begingroup$ rot13(Vf gurer n ernfba jul lbh'ir jevggra "n" naq abg "?") $\endgroup$
    – Prim3numbah
    Commented Feb 19, 2020 at 10:21
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    $\begingroup$ term "a" was a big give away $\endgroup$
    – Dmitry Kamenetsky
    Commented Feb 19, 2020 at 23:02
  • $\begingroup$ Your title says 7 numbers, but everywhere else suggests 6. $\endgroup$
    – L. F.
    Commented Feb 20, 2020 at 1:48
  • $\begingroup$ @L.F. thanks for the comment.... will fix $\endgroup$
    – tom
    Commented Feb 20, 2020 at 10:29
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    $\begingroup$ @DmitryKamenetsky -- Ahh yes. I always find it hard to find a balance between presenting an interesting challenge and making it too easy or too hard. Fair comment. $\endgroup$
    – tom
    Commented Feb 20, 2020 at 10:33

1 Answer 1

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The rule of the sequence is:

Write each square number in hexadecimal and reverse it.

Example & Answer:

0 = 0
1 = 1
4 = 4
9 = 9
16 = 0, 1
25 = 9, 1
36 = 4, 2
49 = 1, 3
64 = 0, 4
81 = 1, 5
100 = 4, 6
121 = 9, 7
144 = 0, 9
169 = 9, a (a represents 10 in hexadecimal)
196 = 4, c
225 = 1, e
256 = 0, 0, 1

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  • $\begingroup$ Congratulations :-), nice explanation, well done! $\endgroup$
    – tom
    Commented Feb 20, 2020 at 10:34

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