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

0,1

Comments

For more info see A266201-A266202.

Links

Table of n, a(n) for n=0..64.

Example

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.

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}]

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;

Sequence in context: A256381 A272975 A190495 * A093330 A071247 A025006

Adjacent sequences: A271985 A271986 A271987 * A271989 A271990 A271991

Keyword

nonn,fini

Author

Natan Arie Consigli, May 21 2016

Status

approved