I need a solution (script?) that would allow me to search a text field containing one long string for the presence of a sequence. I've read that Filemaker will only search the first 20 characters in a word, and 60 characters total. Can one make a script that would search the first left 20, then positions 10 - 30, then 20 -40, etc. Or is this not possible?

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Not exactly true, you are confusing two different things. FileMaker only INDEXES the first 20 characters of a contiguous string in a text field. Searching for a string can be done with a calculation and will work up to the maximum length of a text field (64K characters).

Flag (number) = PatternCount(Field, "abcxyz") > 0

-bd

Filemaker will index "words" up to 20 characters, and "lines" up to 60 characters. A "word" is a series of characters unbroken by spaces. A "line" is a series of words unbroken by a paragraph character.

LiveOak's solution is a good one if you are looking for a specific sequence of characters. If you are doing more generic searching, then you will need to make sure that you setup you data with the restrictions in mind.