# 22, 38, 54, 26, 42, 58, 30, 46, 62

Happy 2010!

Any guesses on the meaning of the sequence of numbers in the title (it is a bit arbitrary)? Leave them in the comments. No prizes but smug self-satisfaction.

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• #### Peter Rowlett

Peter Rowlett teaches mathematics at university and is interested in maths education and communicating maths. His column at The Aperiodical is Travels in a Mathematical World.

### 5 Responses to “22, 38, 54, 26, 42, 58, 30, 46, 62”

1. SomeBeans

I’ve got as far as working out that the difference between consecutive terms is 16 on the rising and 28 on the falling.

28 is the length of the lunar month.

2. Rock Hyrax

The first day of the year was (as you said) a binary number. Convert to decimal and you get 22.

Today is 3 days onwards so lets make three triples. Today is the 4th, so add 4 to get the first numbers of the second and third triples and 26 and 30. 2^4 is 16, so add 16 twice to the first number of each triple to get all nine numbers.

And I doubt that sort of argument will convince anyone any more than it did my boss ten years ago…

3. Peter Rowlett

@SomeBeans: Well spotted, but these are coincidental patterns.

@Rock Hyrax: On the right lines…

16 is caused by 01abcd->10abcd and 10abcd->11abcd being increases of 16. -28 is caused by reversing the two operations above (to give -32) then performing a similar change on the middle digits, giving an increase of 4.

4. Vincent

When converted to binary, they can be split into day, month and year (2 digit)

010110 1 Jan 2010
100110 10 Jan 2010
110110 11 Jan 2010
011010 1 Oct 2010
101010 10 Oct 2010
111010 11 Oct 2010
011110 1 Nov 2010
101110 10 Nov 2010
111110 11 Nov 2010

Those are the only dates in 2010 where the day and month are only 1′s or 0′s.

Credit to my friend Justin (justinlee.sg)