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A271556 a(n) = G_n(9), where G is the Goodstein function defined in A266201.

%I A271556 #19 Jan 11 2020 15:57:47
%S A271556 9,81,1023,9842,140743,2471826,50333399,1162263921,30000003325,
%T A271556 855935016215,26748301350411,908625319783885,33336020476682897,
%U A271556 1313681671142588955,55340232221128667935,2481720785659010308168,118039224225889612744771,5935258966980940767393628
%N A271556 a(n) = G_n(9), where G is the Goodstein function defined in A266201.
%H A271556 Nicholas Matteo, <a href="/A271556/b271556.txt">Table of n, a(n) for n = 0..384</a>
%H A271556 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.
%e A271556 G_1(9) = B_2(9)-1 = B_2(2^(2+1)+1)-1 = 3^(3+1) + 1-1 = 81;
%e A271556 G_2(9) = B_3(3^(3+1))-1 = 4^(4+1)-1 = 1023;
%e A271556 G_3(9) = B_4(3*4^4 + 3*4^3 + 3*4^2 + 3*4 + 3)-1 = 3*5^5 + 3*5^3 + 3*5^2 + 3*5 + 3-1 = 9842;
%e A271556 G_4(9) = B_5(3*5^5 + 3*5^3 + 3*5^2 + 3*5 + 2)-1 = 3*6^6 + 3*6^3 + 3*6^2 + 3*6 + 2-1 = 140743;
%e A271556 G_5(9) = B_6(3*6^6 + 3*6^3 + 3*6^2 + 3*6 + 1)-1 = 3*7^7 + 3*7^3 + 3*7^2 + 3*7 + 1-1 = 2471826;
%e A271556 G_6(9) = B_7(3*7^7 + 3*7^3 + 3*7^2 + 3*7)-1 = 3*8^8 + 3*8^3 + 3*8^2 + 3*8-1 = 50333399.
%o A271556 (PARI) lista(nn) = {print1(a = 9, ", "); 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, ", "); ); }
%Y A271556 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), A266201: G_n(n).
%K A271556 nonn,fini
%O A271556 0,1
%A A271556 _Natan Arie Consigli_, Apr 10 2016