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import FormalConjecturesUtilAscending descending base exponent transform of squares
a n is $\sum_{i=1}^n (i^2)^((n-i+1)^2)$.
References:
namespace OeisA113257a n is the ascending descending base exponent transform of squares
def a (n : ℕ) : ℕ :=
∑ i ∈ Finset.Icc 1 n, (i ^ 2) ^ ((n - i + 1) ^ 2)@[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 = 5 := ⊢ a 2 = 5 All goals completed! 🐙@[category test, AMS 11]
theorem a_3 : a 3 = 266 := ⊢ a 3 = 266 All goals completed! 🐙@[category test, AMS 11]
theorem a_4 : a 4 = 268722 := ⊢ a 4 = 268722 All goals completed! 🐙@[category test, AMS 11]
theorem a_5 : a 5 = 4682453347 := ⊢ a 5 = 4682453347 All goals completed! 🐙The smallest prime in this sequence is $a(2) = 5$. What is the next prime?
@[category research open, AMS 11]
theorem conjecture1 :
answer(sorry) = a (sInf {n : ℕ | 2 < n ∧ (a n).Prime}) := ⊢ sorry = a (sInf {n | 2 < n ∧ Nat.Prime (a n)})
All goals completed! 🐙What is the first square value after 1?
@[category research open, AMS 11]
theorem conjecture2 :
answer(sorry) = a (sInf {n : ℕ | 1 < n ∧ IsSquare (a n)}) := ⊢ sorry = a (sInf {n | 1 < n ∧ IsSquare (a n)})
All goals completed! 🐙end OeisA113257