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There are infinitely many possible number sequences, and infinitely many numbers which can appear in those sequences. Any and every number can appear in a number sequence.
A single number, such as 1531513 does not define a sequence. Furthermore, according to Wittgenstein's Finite Rule Paradox every finite sequence of numbers can be a described in infinitely many ways and so can be continued any of these ways - some simple, some complicated but all equally valid.
Any single digit number is a palindrome. The Fibonacci sequence consists of infinitely many numbers so 8, being only one number, cannot be the Fibonacci sequence.
I doubt that there is one unique sequence that answers this question. Infinitely many is infinitely many. How about the number line as one possible answer?