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A271559
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a(n) = G_n(12), where G is the Goodstein function defined in A266201.
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7
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12, 107, 1065, 15685, 280019, 5764910, 134217867, 3486784574, 100000000211, 3138428376974, 106993205379371, 3937376385699637, 155568095557812625, 6568408355712891083, 295147905179352826375, 14063084452067724991593, 708235345355337676358285, 37589973457545958193356327
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OFFSET
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0,1
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COMMENTS
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Goodstein's theorem shows that such sequence converges to zero for any starting value.
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LINKS
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EXAMPLE
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G_1(12) = B_2(12)-1 = B_2(2^(2+1)+2^2)-1 = 3^(3+1)+3^3-1 = 107;
G_2(12) = B_3(3^(3+1)+2*3^2+2*3+2)-1 = 4^(4+1)+2*4^2+2*4+2-1 = 1065;
G_3(12) = B_4(4^(4+1)+2*4^2+2*4+1)-1 = 5^(5+1)+2*5^2+2*5+1-1 = 15685;
G_4(12) = B_5(5^(5+1)+2*5^2+2*5)-1 = 6^(6+1)+2*6^2+2*6-1 = 280019;
G_5(12) = B_6(6^(6+1)+2*6^2+6+5)-1 = 7^(7+1)+2*7^2+7+5-1 = 5764910;
G_6(12) = B_7(7^(7+1)+2*7^2+7+4)-1 = 8^(8+1)+2*8^2+8+4-1 = 134217867;
G_7(12) = B_8(8^(8+1)+2*8^2+8+3)-1 = 9^(9+1)+2*9^2+9+3-1 = 3486784574.
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PROG
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(PARI) lista(nn) = {print1(a = 12, ", "); for (n=2, nn, pd = Pol(digits(a, n)); q = sum(k=0, poldegree(pd), if (c=polcoeff(pd, k), c*x^subst(Pol(digits(k, n)), x, n+1), 0)); a = subst(q, x, n+1) - 1; print1(a, ", "); ); }
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CROSSREFS
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Cf. A056193: G_n(4), A059933: G_n(16), A211378: G_n(19), A215409: G_n(3), A222117: G_n(15), A266204: G_n(5), A266205: G_n(6), A271554: G_n(7), A271555: G_n(8), A271556: G_n(9), A271557: G_n(10), A271558: G_n(11), A266201: G_n(n).
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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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