Problem 3012. Self-similarity 3 - Every other pair of terms

Created by goc3

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Self-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the <a href = "https://oeis.org/selfsimilar.html">OEIS page</a> for more information.In this problem, you are to check if the sequence is self-similar by every other pair of terms. The problem set assumes that you start with the first element pair and then take every other element pair thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.For example,<ul><li>seq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3]</li><li>seq_every_other_pair = [0, 1, , , 1, 2, , , 1, 2, , , 2, 3, , , 1, 2, , ] (extra commas are instructional and should not be in the every-other series)</li><li>seq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2]</li></ul>Since seq_every_other_pair = seq_orig_first_half, the set is self-similar.This problem is related to <a href = "https://www.mathworks.com/matlabcentral/cody/problems/3010-self-similarity-1-every-other-term">Problem 3010</a> and <a href = "https://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term">Problem 3011</a>.

Self-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the <https://oeis.org/selfsimilar.html OEIS page> for more information.

In this problem, you are to check if the sequence is self-similar by every other pair of terms. The problem set assumes that you start with the first element pair and then take every other element pair thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.

For example,

* seq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3]
* seq_every_other_pair = [0, 1, , , 1, 2, , , 1, 2, , , 2, 3, , , 1, 2, , ] (extra commas are instructional and should not be in the every-other series) 
* seq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2]

Since seq_every_other_pair = seq_orig_first_half, the set is self-similar.

This problem is related to <https://www.mathworks.com/matlabcentral/cody/problems/3010-self-similarity-1-every-other-term Problem 3010> and <https://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term Problem 3011>.

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Jean-Marie Sainthillier on 16 Feb 2015

I discover this notation (the end in the mod)

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Problem 3012. Self-similarity 3 - Every other pair of terms

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