What looks like a harmless number puzzle becomes a test of expressive power: each term is the sum of the two before it, beginning 1, 1. The challenge is to recognize Fibonacci-like sequences when numbers are encoded as runs of @ symbols. section 5.13
1 1 2 3 5 8 13 21 34 55 89 144
The opening terms make the recursive pattern visible before the sequence is translated into a string-matching problem. section 5.13
A regular expression must distinguish valid encodings such as “@ @ @@ @@@ @@@@@” from near misses, while also handling Fibonacci-like sequences that begin with other two values. That generalization connects Fibonacci numbers to Lucas sequences, whose initial values are 2 and 1. section 5.13
fibs1 = "@ @ @@ @@@ @@@@@ @@@@@@@@ " #1 fibs2 = "@ @ @@ @@@ @@@@@ " #2 lucas1 = "@@ @ @@@ @@@@ @@@@@@@ @@@@@@@@@@@ " #3 lucas2 = "@@@ @ @@@@ @@@@@ @@@@@@@@@ @@@@@@@@@@@@@@ " #4 wrong1 = "@ @ @@@ @@@@ @@@@@@@ @@@@@@@@@@@ " #5 wrong2 = "@ @ @@ @@@ @@@@ @@@@@@@ " #6 wrong3 = "@ @ @@ @@@@ @@@@@@ " #7
The candidate strings provide positive, generalized, and deliberately wrong cases for testing whether a matcher tracks the recursive relationship rather than superficial repetition. section 5.13
An AI-generated answer may look impressively technical without establishing correctness. Its proposed pattern uses anchors, noncapturing groups, and lookaheads, so the useful next move is to test it against valid Fibonacci prefixes, Lucas variants, and wrong strings instead of trusting its explanation. section 5.15 section 5.13
