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%I #14 Jan 11 2020 15:57:47
%S 13,108,1279,16092,280711,5765998,134219479,3486786855,100000003325,
%T 3138428381103,106993205384715,3937376385706415,155568095557821073,
%U 6568408355712901455,295147905179352838943,14063084452067725006646,708235345355337676376131,37589973457545958193377292
%N a(n) = G_n(13), where G is the Goodstein function defined in A266201.
%H Nicholas Matteo, <a href="/A271560/b271560.txt">Table of n, a(n) for n = 0..383</a>
%e G_1(13) = B_2(13)-1 = B_2(2^(2+1)+2^2+1)-1 = 3^(3+1)+3^3+1-1 = 108;
%e G_2(13) = B_3(3^(3+1)+3^3)-1 = 4^(4+1)+4^4-1 = 1279;
%e G_3(13) = B_4(4^(4+1)+3*4^3+3*4^2+3*4+3)-1 = 5^(5+1)+3*5^3+3*5^2+3*5+3-1 = 16092;
%e G_4(13) = B_5(5^(5+1)+3*5^3+3*5^2+3*5+2)-1 = 6^(6+1)+3*6^3+3*6^2+3*6+2-1 = 280711;
%e G_5(13) = B_6(6^(6+1)+3*6^3+3*6^2+3*6+1)-1 = 7^(7+1)+3*7^3+3*7^2+3*7+1-1 = 5765998;
%e G_6(13) = B_7(7^(7+1)+3*7^3+3*7^2+3*7)-1 = 8^(8+1)+3*8^3+3*8^2+3*8-1 = 134219479;
%e G_7(13) = B_8(8^(8+1)+3*8^3+3*8^2+2*8+7)-1 = 9^(9+1)+3*9^3+3*9^2+2*9+7-1 = 3486786855.
%o (PARI) lista(nn) = {my(a=13); print1(a, ", "); for (n=2, nn, my(pd = Pol(digits(a, n)), q = sum(k=0, poldegree(pd), my(c=polcoeff(pd, k)); if (c, c*x^subst(Pol(digits(k, n)), x, n+1), 0))); a = subst(q, x, n+1) - 1; print1(a, ", "); ); }
%Y 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), A271559: G_n(12), A266201: G_n(n).
%K nonn,fini
%O 0,1
%A _Natan Arie Consigli_, Apr 11 2016
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