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Copyright 2026 The Formal Conjectures Authors.
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you may not use this file except in compliance with the License.
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import FormalConjecturesUtil
namespace OeisA113010open Nata n is the {Number of digits of n} raised to the power of {the sum of the digits of n}.
def a (n : ℕ) : ℕ :=
((10).digits n).length ^ (List.sum ((10).digits n))@[category test, AMS 11]
theorem a_0 : a 0 = 1 := ⊢ a 0 = 1 All goals completed! 🐙@[category test, AMS 11]
theorem a_1 : a 1 = 1 := ⊢ a 1 = 1 All goals completed! 🐙@[category test, AMS 11]
theorem a_2 : a 2 = 1 := ⊢ a 2 = 1 All goals completed! 🐙@[category test, AMS 11]
theorem a_3 : a 3 = 1 := ⊢ a 3 = 1 All goals completed! 🐙@[category test, AMS 11]
theorem a_4 : a 4 = 1 := ⊢ a 4 = 1 All goals completed! 🐙$n=1$ and $32$ are two fixed points. Are there any others?
@[category research open, AMS 11]
theorem conjecture : answer(sorry) ↔ ∀ n : ℕ, a n = n ∧ n > 0 → n = 1 ∨ n = 32 := ⊢ True ↔ ∀ (n : ℕ), a n = n ∧ n > 0 → n = 1 ∨ n = 32
All goals completed! 🐙end OeisA113010