# An omalonumerophobic's number sequence

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.

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

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.

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

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

• .5 is not an integer, as required by the question.
– Rubio
Sep 23 '17 at 20:03