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Find all seven terms of the number sequence,

a1, a2, a3, a4, a5, a6, a7

given that

  • each successive term is exactly twice the value of the previous term
  • no even digits are used in writing the terms


The ai are integers written in decimal notation.

Thanks to @GOTO 0 for the inspiration.

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    $\begingroup$ Yes - thanks boboquack - your words are good (and help to rule out more lateral thinking). $\endgroup$
    – Tom
    Sep 21 '17 at 4:13
  • $\begingroup$ @Tom they're your words :P $\endgroup$
    – boboquack
    Sep 21 '17 at 4:19
  • $\begingroup$ Decimal notation definitely means base 10, correct? $\endgroup$
    – Hugh Meyers
    Sep 22 '17 at 12:30
  • $\begingroup$ Yes, base ten decimal representation. $\endgroup$
    – Tom
    Sep 22 '17 at 12:44
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The numbers could be

$5, 9.\bar{9},19.\bar{9},39.\bar{9},79.\bar{9},159.\bar{9},319.\bar{9}$.

It's easy to check that all the conditions are satisfied; however, I don't know if this set is unique.

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Well, based on the answer of Ankonganit, perhaps, here is another one:

.5, 1, 1.9999..., 3.9999..., 7.9999..., 15.9999..., 31.9999...

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    $\begingroup$ .5 is not an integer, as required by the question. $\endgroup$
    – Rubio ♦
    Sep 23 '17 at 20:03

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