Triangular and Fibonacci Running Equality Expressions Generator

Equality partitions split the digit run into contiguous, non-overlapping chunks (for example, a double equality may split 9 digits into three groups of 3) — every chunk still uses its digits exactly once, and no digit is ever shared between chunks. Double and triple equalities add search time because more partition points must be checked.

This only sets how many equations are shown per k when the search first finishes — every distinct equation the search actually finds for a k is stored and can be reached via the "showing" +/- control below, and downloads always include the full stored set, not just what's currently displayed. Results are ranked by a transparent complexity score, with the simplest verified identities first.

Interval mode retunes the search to favor values near your chosen range instead of small numbers — this is what makes ranges like 1010–1033 reachable, at the cost of no longer finding much outside it. Only the digit runs selected above are searched, and only k values inside [From, To] are kept.

Exact-target mode concentrates the search on one chosen value of k and retains only identities that pass a strict independent numerical recheck.