A271988 g_n(7) where g is the weak Goodstein function defined in A266202.

7, 12, 19, 27, 37, 49, 63, 69, 75, 81, 87, 93, 99, 105, 111, 116, 121, 126, 131, 136, 141, 146, 151, 156, 161, 166, 171, 176, 181, 186, 191, 195, 199, 203, 207, 211, 215, 219, 223, 227, 231, 235, 239, 243, 247, 251, 255, 259, 263, 267, 271, 275, 279, 283, 287, 291, 295, 299, 303, 307, 311, 315, 319, 322, 325

Offset: 0

Author

Natan Arie Consigli, May 21 2016

Keywords

• nonn
• fini

Comments

For more info see A266201-A266202.

Examples

			g_1(7)= b_2(7)-1 = b_2(2^2+2+1)-1 = 3^2+3+1-1 = 12;
g_2(7) = b_3(3^2+3)-1 = 4^2+4-1 = 19;
g_3(7) = b_4(4^2+3)-1 = 5^2+3-1 = 27;
g_4(7) = b_5(5^2+2)-1 = 6^2+2-1 = 37;
g_5(7) = b_6(6^2+1)-1 = 7^2+1-1 = 49;
g_6(7) = b_7(7^2)-1 = 8^2-1 = 63;
g_7(7) = b_8(7*8+7)-1 = 7*9+7-1 = 69;
...
g_2045(7) = 0.
		

Crossrefs

Cf. A271554: G_n(7).

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;

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, 7], {n, 0, 64}]