%I #11 Jan 11 2020 15:57:47
%S 6,11,17,25,35,39,43,47,51,55,59,62,65,68,71,74,77,80,83,86,89,92,95,
%T 97,99,101,103,105,107,109,111,113,115,117,119,121,123,125,127,129,
%U 131,133,135,137,139,141,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161
%N g_n(6) where g is the weak Goodstein function defined in A266202.
%C For more info see A266201-A266202.
%H Michael De Vlieger, <a href="/A271987/b271987.txt">Table of n, a(n) for n = 0..381</a>
%e g_1(6) = b_2(6)-1 = b_2(2^2+2)-1 = 3^2+3-1 = 11;
%e g_2(6) = b_3(3^2+2)-1 = 4^2+2-1 = 17;
%e g_3(6) = b_4(4^2+1)-1 = 5^2+1-1 = 25;
%e g_4(6) = b_5(5^2)-1 = 6^2-1 = 35;
%e g_5(6) = b_6(5*6+5)-1 = 5*7+5-1 = 39;
%e g_6(6) = b_7(5*7+4)-1 = 5*8+4-1 = 43;
%e g_7(6) = b_8(5*8+3)-1 = 5*9+3-1 = 47;
%e g_8(6) = b_9(5*9+2)-1 = 5*10+2-1 = 51;
%e g_9(6) = b_10( 5*10+1)-1 = 5*11+1-1= 55;
%e g_10(6) = b_11(5*11)-1 = 5*12-1 = 59;
%e g_11(6) = b_12(4*12+11)-1 = 4*13+11-1= 62;
%e g_12(6) = b_13(4*13+10)-1 = 4*14+10-1 = 65;
%e ...
%e g_381(6) = 0.
%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, 6], {n, 0, 64}] (* _Michael De Vlieger_, May 17 2016 *)
%Y Cf. A266205: G_n(6).
%Y Weak Goodstein sequences: A137411: g_n(11); A265034: g_n(266); A267647: g_n(4); A267648: g_n(5); 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 15 2016