I am having problems figuring out the following sequence:

2,4,9,6,5,6,____,____,____,...

We were able to guess that the pattern simply started to reverse itself,
but I was wondering if there were other possibilities.

Thank you,
Mike

 


Hi Mike,

I can make sense of 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, ... These are the unit digits of the squares 1, 4, 9, 16, 25, 36, ...

As for 2, 4, 9, 6, 5, 6, when I feed it into the online encyclopedia of integer sequences
http://www.research.att.com/~njas/sequences/Seis.html, it spits out the
sequence

0, 6, 2, 9, 2, 3, 3, 2, 1, 3, 1, 3, 8, 6, 0, 7, 5, 8,
7, 7, 8, 4, 4, 5, 8, 2, 2, 0, 3, 3, 2, 4, 6, 9, 6, 3,
6, 7, 9, 4, 4, 2, 2, 8, 0, 6, 1, 5, 9, 2, 1, 7, 1, 0,
4, 6, 4, 1, 8, 7, 7, 4, 0, 5, 2, 2, 1, 6, 1, 4, 5, 2,
0, 9, 3, 6, 5, 7, 0, 2, 0, 4, 2, 4, 9, 6, 5, 6, 2, 7,
5, 2, 6, 2, 3, 7, 3, 6, 5, 2, 1, 9, 5, 3, 1

which is the start of the decimal expansion of the only root of Sum_{p prime} xp = 0. You can see 2, 4, 9, 6, 5, 6 on the fifth line, roughly in the middle. But then again, is this meaningful? In the 10 million first digits of the square root of 2 posted at http://antwrp.gsfc.nasa.gov/htmltest/gifcity/sqrt2.10mil you find 249656
many times, not counting occurences separated by line breaks.

Claude