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A337805 Lazy Beaver Problem: a(n) is the smallest positive number of steps a(n) such that no n-state Turing machine halts in exactly a(n) steps on an initially blank tape.

Original entry on oeis.org

2, 7, 22, 72, 427
Offset: 1

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Zachary Vance, Sep 23 2020

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Comments

This sequence and the Busy Beaver (A060843) problem are closely related. Turing machines and the number of steps taken by a Turing machine on an initially blank tape are defined in A060843.
This sequence is computable, while the Busy Beaver problem is uncomputable.
a(n) - 1 <= BB(n), where BB(n) = A060843(n).
a(n) - 1 <= A107668 * 4^(2n), the number of uniquely behaving n-state Turing machines with 2 symbols, by the pigeonhole principle.

Examples

			For n = 2, there exist 2-state Turing machines which halt in exactly {1, 2, 3, 4, 5, 6} steps (and for no other number of steps) given an initially empty input tape. a(2) = 7 is defined as the lowest positive integer not present in that set of possible step lengths.

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Crossrefs

Known upper bounds of a(n) - 1 are A028444, A004147, and A141475.

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