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SQLite search with text vs numeric field
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Index depth probably won't increase by nearly that much.

Fan out depends mostly on the usable record size / (size of the key plus the size of a record pointer (4 bytes in SQLite, I believe)). That reduces the ratio to about 11.

Depth depends on the log of the fan-out, if the index record size is 1k or more, the depth difference probably won't exceed a factor of four.

Of course an index that is 11 times as large is going to have more cache misses, and predicting the effect of that is black magic, so as Keith wisely said, "give it a try."