A300404 Smallest integer k such that the largest term in the Goodstein sequence starting at k is > n.

2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset: 0

Author

Felix Fröhlich, Mar 05 2018

Keywords

• nonn

Comments

The sequence apparently grows very slowly.

Is the sequence unbounded?

Links

• Wikipedia, Goodstein's theorem

Crossrefs

Cf. A215409, A056193, A266204, A266205, A271554, A059933, A300402, A300403.

Programs

PARI

\\ define the function bump() as in A059933
a(n) = my(k=1, x=k, step=2); while(1, x=bump(x, step)-1; step++; if(x > n, return(k)); if(x==0, k++; x=k; step=2))