Exact Lucas Number Calculator

Start with L(0) = 2 and L(1) = 1, then add the two preceding terms until reaching index n. Lucas and Fibonacci numbers share a recurrence but use different starting values. Inputs remain whole numbers inside the displayed domain, and the page never rounds a decimal into an accepted integer. This keeps the reported result tied to one explicit mathematical definition rather than an unstated convention.

The output is indexed from zero and follows the Lucas initial pair, not the Fibonacci initial pair. Add the two preceding displayed terms to reproduce the requested term. Reuse the displayed recurrence, congruence, or counting identity with the same inputs. The verification evidence checks this calculator's result, but it does not establish assumptions or conclusions outside the stated mathematical domain.

The index is capped at 76 because the next Lucas terms exceed reliable exact-number storage in this implementation. The cap prevents later integer terms from being silently rounded. A finite limit prevents browser stalls and avoids presenting an unsafe floating-point integer as exact. Work beyond that limit belongs in arbitrary-precision software with explicit resource controls and independent validation.