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A271989 g_n(8) where g is the weak Goodstein function defined in A266202. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

For more info see A266201-A266202.

LINKS

Table of n, a(n) for n=0..55.

EXAMPLE

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.

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}]

CROSSREFS

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;

Sequence in context: A265104 A328205 A304910 * A069952 A031085 A224481

Adjacent sequences:  A271986 A271987 A271988 * A271990 A271991 A271992

KEYWORD

nonn,fini

AUTHOR

Natan Arie Consigli, May 22 2016

STATUS

approved

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Last modified September 20 10:24 EDT 2020. Contains 337264 sequences. (Running on oeis4.)