A271989 g_n(8) where g is the weak Goodstein function defined in A266202.

8, 26, 41, 60, 83, 109, 139, 173, 211, 253, 299, 348, 401, 458, 519, 584, 653, 726, 803, 884, 969, 1058, 1151, 1222, 1295, 1370, 1447, 1526, 1607, 1690, 1775, 1862, 1951, 2042, 2135, 2230, 2327, 2426, 2527, 2630, 2735, 2842, 2951, 3062, 3175, 3290, 3407, 3525, 3645, 3767, 3891, 4017, 4145, 4275, 4407, 4541

Offset: 0

Author

Natan Arie Consigli, May 22 2016

Keywords

• nonn
• fini

Comments

For more info see A266201-A266202.

Examples

			g_1(8) = b_2(8)-1 = b_2(2^3)-1 = 3^3-1 = 26;
g_2(8) = b_3(2*3^2+2*3+2)-1 = 2*4^2+2*4+2-1 = 41;
g_3(8) = b_4(2*4^2+2*4+1)-1 = 2*5^2+2*5+1-1 = 60;
g_4(8) = b_5(2*5^2+2*5)-1 = 2*6^2+2*6-1 = 83;
g_5(8) = b_6(2*6^2+6+5)-1 = 2*7^2+7+5-1 = 109;
g_6(8) = b_7(2*7^2+7+4)-1 = 2*8^2+8+4-1 = 139;
g_7(8) = b_8(2*8^2+8+3)-1 = 2*9^2+9+3-1 = 173;
g_8(8) = b_9(2*9^2+9+2)-1 = 2*10^2+10+2-1 = 211;
g_9(8) = b_10(2*10^2+10+1)-1 = 2*11^2+11+1-1 = 253;
g_10(8) = b_11(2*11^2+11)-1 = 2*12^2+12-1 = 299.
		

Crossrefs

Essentially the same as A056193.

Cf. G_n(8): A271555.

Weak Goodstein sequences: A137411: g_n(11); A265034: g_n(266); A267647: g_n(4); A267648: g_n(5); A271987: g_n(6); A271988: g_n(7); 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, 8], {n, 0, 55}]