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%I #25 Jan 11 2020 15:57:47
%S 6,29,257,3125,46655,98039,187243,332147,555551,885775,1357259,
%T 2011162,2895965,4068068,5592391,7542974,10003577,13068280,16842083,
%U 21441506,26995189,33644492,41544095,50862597,61783119,74503901,89238903,106218405,125689607,147917229
%N a(n) = G_n(6), where G is the Goodstein function defined in A266201.
%H Nicholas Matteo, <a href="/A266205/b266205.txt">Table of n, a(n) for n = 0..10000</a>
%H R. L. Goodstein, <a href="http://www.jstor.org/stable/2268019">On the Restricted Ordinal Theorem</a>, The Journal of Symbolic Logic 9, no. 2 (1944), 33-41.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Goodstein%27s_theorem#Goodstein_sequences">Goodstein sequence</a>
%e G_1(6) = B_2(6) - 1 = B_2(2^2 + 2) - 1 = 3^3 + 3 - 1 = 29;
%e G_2(6) = B_3(G_1(6)) - 1 = B_3(3^3 + 2) - 1 = 4^4 + 2 - 1 = 257;
%e G_3(6) = B_4(G_2(6)) - 1 = 5^5 + 1 - 1 = 3125;
%e G_4(6) = B_5(G_3(6)) - 1 = 6^6 - 1 = 46655;
%e G_5(6) = B_6(G_4(6)) - 1 = 5*7^5 + 5*7^4 + 5*7^3 + 5*7^2 + 5*7 + 5 - 1 = 98039.
%o (PARI) lista(nn) = {print1(a = 6, ", "); 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, ", "););} \\ _Michel Marcus_, Feb 22 2016
%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), A059936: G_5(n), A266201: G_n(n).
%K nonn,fini
%O 0,1
%A _Natan Arie Consigli_, Jan 23 2016
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