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A271989
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g_n(8) where g is the weak Goodstein function defined in A266202.
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3
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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
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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(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.
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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, 8], {n, 0, 55}]
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CROSSREFS
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KEYWORD
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nonn,fini
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AUTHOR
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STATUS
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approved
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