A300402 -id:A300402 - cp's OEIS frontend

A300403 Smallest integer i such that SSCG(i) >= n.

0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 1

Felix Fröhlich, Mar 05 2018

nonn

The sequence grows very slowly.
A subcubic graph is a graph where each vertex has degree <= 3 (cf. Baaz et al., 2011, p. 419).
SSCG(n) gives the length of the longest sequence of simple subcubic graphs G_1, G_2, ..., G_i such that each G_i has at most i+n vertices and G_i is not a graph minor of G_j for any j > i.

			SSCG(0) = 2, so a(n) = 0 for n <= 2.
SSCG(1) = 5, so a(n) = 1 for 3 <= n <= 5.
SSCG(2) = 3*2^(3*2^95)-8 ~ 10^(3.5775*10^28), so a(n) = 2 for 6 <= n <= 3*2^(3*2^95)-8.

M. Baaz, C. H. Papadimitriou, H. W. Putnam, D. S. Scott and C. L. Harper, Jr., Kurt Gödel and the Foundations of Mathematics: Horizons of Truth, Cambridge University Press, 2011, ISBN 978-0-521-76144-4.
Eric Weisstein's World of Mathematics, Simple Graph
Wikipedia, Friedman's SSCG function
Wikipedia, Graph minor

Cf. A090529, A300402, A300404.

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

Original entry on oeis.org

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

Felix Fröhlich, Mar 05 2018

nonn

The sequence apparently grows very slowly.

Is the sequence unbounded?

Wikipedia, Goodstein's theorem

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

\\ 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))

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A300403 Smallest integer i such that SSCG(i) >= n.

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