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A268689 Let f(n) = maximal value of the weak Goodstein function g_k(n) for k >= 0; then a(n) = minimal value of k such that g_k(n) = f(n). 3
0, 0, 0, 0, 4, 14, 94, 510 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

g_k(n) is the weak Goodstein function defined in A266202.

LINKS

Table of n, a(n) for n=0..7.

EXAMPLE

g_1(4) = b_2(4)-1 = b_2(2^2)-1 = 3^2-1 = 8;

g_2(4) = b_3(2*3+2)-1 = 2*4 + 2-1 = 9;

g_3(4) = b_4(2*4 + 1 ) -1 = 2*5 + 1-1 = 10;

g_4(4) = b_5(2*5) -1= 2*6 - 1 = 11;

g_5(4) = b_6(6+5)-1 = 7+5-1 = 11;

g_6(4) = b_7(7+4)-1 = 8+4-1 = 11;

g_7(4) = b_8(8+3)-1 = 9+3-1 = 11;

g_8(4) = b_9(9+2)-1 = 10+2-1 = 11;

g_9(4) = b_10(10+1)-1 = 11+1-1 = 11;

g_10(4) = b_11(11)-1 = 12-1 = 11;

g_11(4) = b_12(11)-1 = 11-1 = 10;

g_12(4) = b_13(10)-1 = 10-1 = 9;

g_13(4) = b_14(9)-1 = 9-1 = 8;

g_21(4) = 0;

So a(4) = 4.

PROG

(PARI) g(n, k) = {if (n == 0, return (k)); wn = k; for (k=2, n+1, pd = Pol(digits(wn, k)); wn = subst(pd, x, k+1) - 1; ); wn; }

a(n) = {vg = []; ok = 1; ns = 0; while(ok, newg = g(ns, n); vg = concat(vg, newg); if (newg <= 0, ok = 0); ns++; ); vmax = vecmax(vg); k = 1; while (vg[k] != vmax, k++); k--; } \\ Michel Marcus, Apr 03 2016

CROSSREFS

Cf. A266203, A268687, A268688.

Sequence in context: A331637 A190481 A316414 * A299199 A209322 A110302

Adjacent sequences:  A268686 A268687 A268688 * A268690 A268691 A268692

KEYWORD

nonn,hard

AUTHOR

Natan Arie Consigli, Apr 03 2016

EXTENSIONS

a(7) from Michel Marcus, Apr 03 2016

STATUS

approved

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Last modified September 20 10:04 EDT 2020. Contains 337264 sequences. (Running on oeis4.)