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Smallest integer i such that SSCG(i) >= n.
2

%I #10 Apr 16 2018 18:46:24

%S 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,

%T 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,

%U 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2

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

%C The sequence grows very slowly.

%C A subcubic graph is a graph where each vertex has degree <= 3 (cf. Baaz et al., 2011, p. 419).

%C 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.

%H M. Baaz, C. H. Papadimitriou, H. W. Putnam, D. S. Scott and C. L. Harper, Jr., <a href="https://books.google.com/books?id=Tg0WXU5_8EgC&amp;pg=PA419">Kurt Gödel and the Foundations of Mathematics: Horizons of Truth</a>, Cambridge University Press, 2011, ISBN 978-0-521-76144-4.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SimpleGraph.html">Simple Graph</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Friedman%27s_SSCG_function">Friedman's SSCG function</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Graph_minor">Graph minor</a>

%e SSCG(0) = 2, so a(n) = 0 for n <= 2.

%e SSCG(1) = 5, so a(n) = 1 for 3 <= n <= 5.

%e 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.

%Y Cf. A090529, A300402, A300404.

%K nonn

%O 1,6

%A _Felix Fröhlich_, Mar 05 2018