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Math Help - What pattern is this? add 7 or 17

  1. #1
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    What pattern is this? add 7 or 17

    Could anyone please assist me. I have been trying to figure out what this pattern in called. Or if anyone knows any info on it I would appreciate the help. It can start with any number (or so I think). We will start with 1.
    The pattern is add 7 but if the last number is 2, 1 or 0 add 17.

    1, 18, 25, 32, 49, 56, 63, 70, 87, 94
    or
    2, 19, 26, 33, 40, 57, 64, 71, 88, 95

    What I see is the last digit of each number is only used 1 time as the last digit. As well as the first digit. None repeat them selves.

    Would they repeat after 1000 cycles.

    And help is appreciated

    Anna
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  2. #2
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    Hello, Anna!

    The problem is not stated clearly.


    The sequence can start with any number (or so I think).

    The pattern is: add 7 ... but if the last number is 2, 1 or 0, add 17.
    Are we concerned with the last (rightmost) digit?
    . . or the last two digits? . . . or what?


    If we are interested in only the last (rightmost) digit,
    . . then the above condition is redundant, isn't it?
    Whatever the last digit, we add 7.

    \text{The sequence is: }\;\underbrace{1, 8, 5, 2, 9, 6, 3, 0, 7, 4}, \;\underbrace{1, 8,5,2,9 \hdots}

    The cycle repeats itself every ten digit.



    If we are concerned with the last two-digits,

    . . \text{we have: }\;\underbrace{01,18,25,32,49,56,63,70,87,94},\;\u  nderbrace{01, 18, 25, 32, 49 \hdots }<br />

    and we still have a ten-number repeating cycle.



    So what was the question?

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  3. #3
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    7 17

    Apologies if the ? was unclear, as it is not clear to me how to explain it.
    I thank you for the help.

    I was wondering if this was a sort of system like luhn or mod 10.

    Thank you agian.
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