[seqfan] A sequence

Antreas Hatzipolakis anopolis72 at gmail.com
Wed Nov 26 13:07:49 CET 2014


Following is a sequence problem proposed in the Greek Math. magazine
EUCLID (November 1970).

Probably the sequence is not interesting for inclunding in OEIS, but anyway
here it is....

Translation of the problem:

We consider the sequence x_1, x_2, x_3,... x_n,....:

x_1 = 11, x_2 = 32, x_3 = 54, x_4= 78, x_5 = 106, x_6  = 194,....

To find the greatest of the terms of the sequence each one of them is
less that the sum of the two previous terms.

Since the word-by-word translation doesn't make much sense, I explain:

Find the greatest index m such that:

x_m < x_(m-1) + x_(m-2)

Well.... the formula of the sequence is

x_n =  2^(n-1) + 20n - 10

The greatest term in question is x_10 = 702:

x_10 < x_8 + x_9 ie 702  < 278 + 428  = 706

For n >10, we have that x_n > x_(n-1) + x_(n-2).


APH


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