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A267647
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a(n) = g_n(4), where g is the weak Goodstein function defined in A266202.
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10
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4, 8, 9, 10, 11, 11, 11, 11, 11, 11, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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LINKS
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EXAMPLE
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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;
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MATHEMATICA
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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, 4], {n, 0, 21}] (* Michael De Vlieger, Mar 18 2016 *)
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PROG
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(PARI) a(n) = {if (n == 0, return (4)); wn = 4; for (k=2, n+1, pd = Pol(digits(wn, k)); wn = subst(pd, x, k+1) - 1; ); wn; }
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CROSSREFS
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KEYWORD
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nonn,full,fini,easy
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AUTHOR
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STATUS
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approved
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