Erdős problem 342 · problems.science

$a(3) = 4$ : among sums $> 3$ with a unique representation from $\{1,2,3\}$ , the smallest is $4 = 1 + 3$ . The candidate $5 = 2 + 3$ is ruled out by minimality since $4$ has a unique representation.

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7 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

342.lean

Retained formal statement2 of 7

Does Ulam's sequence eventually have periodic differences? That is, is $a(n+1) - a(n)$ eventually periodic?

FormalConjectures/ErdosProblems/342.leanErdos342.erdos_342.parts.ii5 linesExact file

1sorry ↔2  ∀ (a : ℕ → ℕ),3    Erdos342.IsUlamSequence a →4      have d := fun n => ↑(a (n + 1)) - ↑(a n);5      ∃ p > 0, ∀ᶠ (m : ℕ) in Filter.atTop, d (m + p) = d m

OpenStatement only, no proof

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