login
g_n(9) where g is the weak Goodstein function defined in A266202.
3

%I #5 Jan 11 2020 15:57:47

%S 9,27,63,92,127,168,215,267,325,389,459,535,617,705,799,898,1003,1114,

%T 1231,1354,1483,1618,1759,1906,2059,2218,2383,2554,2731,2914,3103,

%U 3297,3497,3703,3915,4133,4357,4587,4823,5065,5313,5567,5827,6093,6365,6643

%N g_n(9) where g is the weak Goodstein function defined in A266202.

%C For more info see A266201-A266202.

%t g[k_, n_] := If[k == 0, n, Total@ Flatten@ MapIndexed[#1 (k + 2)^(#2 - 1) &, Reverse@ IntegerDigits[#, k + 1]] &@ g[k - 1, n] - 1]; Table[g[n, 9], {n, 0, 45}]

%Y Cf. A271556: G_n(9).

%Y Weak Goodstein sequences: A137411: g_n(11); A265034: g_n(266); A267647: g_n(4); A267648: g_n(5); A271987: g_n(6); A266202: g_n(n); A266203: a(n)=k such that g_k(n)=0;

%K nonn,fini

%O 0,1

%A _Natan Arie Consigli_, May 22 2016