ARML, Individual Rounds: Patterns of Palindromes
Channel: Noble Mushtak
Date: 2016-05-15

This is a ARML (American Regions Mathematics League) problem from 2014, Individual Rounds, Problem 5: http://www.arml2.com/arml_2016/public_contest_files/2014_contest_file/2014_Contest_Final_Version.pdf

The operating system used was Ubuntu 15.10: http://www.ubuntu.com/
Also, this was recorded with Kazam: https://apps.ubuntu.com/cat/applications/kazam/
The math writings were made on Emacs: https://www.gnu.org/software/emacs/

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Condensed Writing Solution:
The pattern is palindrome, pailindrome, not-palindrome.
Thus, there is a not-palindrome every 3 terms, so there are 1000/3=333 not-palindromes, so the number of palindromes is 1000-333=667 ANSWER