lean_workbook_plus_40544

⚠️ Retired — specification defect

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

A sequence is defined as follows: $a_1 = 1$ and $a_n = 5a_{n-1} + 6$ for $n > 1$. Find $a_6$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_40544 (a : ℕ → ℕ) (a1 : a 0 = 1) (a_rec : ∀ n, a (n + 1) = 5 * a n + 6) : a 6 = 1561   :=  by sorry

The initial index shifts from a₁ to a₀ and the inserted answer is wrong for either requested index.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Keep a₁=1 and recurrence for n>1, then prove a₆=7811. With zero-based indexing the corresponding a₅=7811 and a₆=39061.

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.