lean_workbook_plus_7353

⚠️ 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.

Let $b_n=a_n^2-n-\frac 12$ . Then $b_4=\frac{7}{36}$ and $b_{n+1}=f_n(b_n)$ , were $f_n(x)=\frac{\frac{5}{4}n^2+n+\frac 14-(n^3-\frac 12 n^2-2n-1)x+x^2}{n^2(n+\frac 12+x)}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_7353  (b : ℕ → ℚ)
  (h₀ : b 4 = 7 / 36)
  (h₁ : ∀ n, b (n + 1) = (5 / 4 * n^2 + n + 1 / 4 - (n^3 - 1 / 2 * n^2 - 2 * n - 1) * b n + b n^2) / (n^2 * (n + 1 / 2 + b n))) :
  b 6 = 7 / 2   :=  by sorry

The source recurrence is applied at zero where its denominator vanishes, forcing values incompatible with b(4).

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

Impose the recurrence only from the actual positive starting index, ordinarily n≥4 after prescribing b(4), and remove the invented b(6)=7/2 answer; if computing b(6) from n=4,5, the supplied recurrence gives243635089/2161134144.

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.