A271987 g_n(6) where g is the weak Goodstein function defined in A266202.

6, 11, 17, 25, 35, 39, 43, 47, 51, 55, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 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

Offset: 0

Author

Natan Arie Consigli, May 15 2016

Keywords

• nonn
• fini

Comments

For more info see A266201-A266202.

Examples

			g_1(6) = b_2(6)-1 = b_2(2^2+2)-1 = 3^2+3-1 = 11;
g_2(6) = b_3(3^2+2)-1 = 4^2+2-1 = 17;
g_3(6) = b_4(4^2+1)-1 = 5^2+1-1 = 25;
g_4(6) = b_5(5^2)-1 = 6^2-1 = 35;
g_5(6) = b_6(5*6+5)-1 = 5*7+5-1 = 39;
g_6(6) = b_7(5*7+4)-1 = 5*8+4-1 = 43;
g_7(6) = b_8(5*8+3)-1 = 5*9+3-1 = 47;
g_8(6) = b_9(5*9+2)-1 = 5*10+2-1 = 51;
g_9(6) = b_10( 5*10+1)-1 = 5*11+1-1= 55;
g_10(6) = b_11(5*11)-1 = 5*12-1 = 59;
g_11(6) = b_12(4*12+11)-1 = 4*13+11-1= 62;
g_12(6) = b_13(4*13+10)-1 = 4*14+10-1 = 65;
...
g_381(6) = 0.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..381

Crossrefs

Cf. A266205: G_n(6).

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;

Programs

Mathematica

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 *)