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A266203 Number of steps k to make g_k(n) converge to zero. 14
0, 1, 3, 5, 21, 61, 381, 2045 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Next term is 3*2^402653211 - 3;

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

For a complete table click the link below, and see table of upper bounds on weak Goodstein sequence.

LINKS

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

Googology Wiki, Weak Goodstein Table

FORMULA

a(n) = k such that g_k(n)=0.

EXAMPLE

Find a(4):

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)=21.

CROSSREFS

Cf. A266202.

Sequence in context: A110026 A235136 A153862 * A264683 A286033 A056803

Adjacent sequences:  A266200 A266201 A266202 * A266204 A266205 A266206

KEYWORD

nonn,hard

AUTHOR

Natan Arie Consigli, Jan 22 2016

STATUS

approved

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Last modified September 20 11:01 EDT 2020. Contains 337264 sequences. (Running on oeis4.)