lean_workbook_plus_63440

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Proved status carries no information about that problem. Do not import this node or use it as a dependency.

Determine the sequence $(a_n)_{n \geq 1}$ where $a_1=1$, $a_2=2$, and $a_{n+1}=a_n+a_{[(n+1)/2]}$ for $n \geq 3$, where $[]$ denotes the integer part. Find a closed-form expression for $a_n$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_63440 (n : ℕ) (f : ℕ → ℕ) (hf: f 1 = 1 ∧ f 2 = 2 ∧ ∀ n ≥ 3, f (n + 1) = f n + f ((n + 1) / 2)) : ∃ g : ℕ → ℕ, ∀ n ≥ 1, f n = g n   :=  by sorry

A closed-form sequence/classification is replaced by existence of an arbitrary equal function.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

Supply a proved explicit expression for f(n), together with any missing initial value needed by the recurrence (the displayed data leave f(3) unspecified). Do not quantify over an arbitrary copy g.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.