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A271555 a(n) = G_n(8), where G is the Goodstein function defined in A266201.

%I A271555 #21 Jan 11 2020 15:57:47
%S A271555 8,80,553,6310,93395,1647195,33554571,774841151,20000000211,
%T A271555 570623341475,17832200896811,605750213184854,22224013651116433,
%U A271555 875787780761719208,36893488147419103751,1654480523772673528938,78692816150593075151501,3956839311320627178248684
%N A271555 a(n) = G_n(8), where G is the Goodstein function defined in A266201.
%H A271555 Nicholas Matteo, <a href="/A271555/b271555.txt">Table of n, a(n) for n = 0..384</a>
%H A271555 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 A271555 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goodstein%27s_theorem#Goodstein_sequences">Goodstein sequence</a>
%e A271555 G_1(8) = B_2(8)-1 = B_2(2^(2+1))-1 = 3^(3+1)-1 = 80;
%e A271555 G_2(8) = B_3(2*3^3+2*3^2+2*3+2)-1 = 2*4^4+2*4^2+2*4+2-1 = 553;
%e A271555 G_3(8) = B_4(2*4^4+2*4^2+2*4+1)-1 = 2*5^5+2*5^2+2*5+1-1 = 6310;
%e A271555 G_4(8) = B_5(2*5^5+2*5^2+2*5)-1 = 2*6^6+2*6^2+2*6-1 = 93395;
%e A271555 G_5(8) = B_6(2*6^6+2*6^2+6+5)-1 = 2*7^7+2*7^2+7+5-1 = 1647195;
%e A271555 G_6(8) = B_7(2*7^7+2*7^2+7+4)-1 = 2*8^8+2*8^2+8+4-1 = 33554571;
%e A271555 G_7(8) = B_8(2*8^8+2*8^2+8+3)-1 = 2*9^9+2*9^2+9+3-1 = 774841151.
%o A271555 (PARI) lista(nn) = {print1(a = 8, ", "); 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 A271555 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), A266201: G_n(n).
%K A271555 nonn,fini
%O A271555 0,1
%A A271555 _Natan Arie Consigli_, Apr 10 2016
%E A271555 a(3) corrected by _Nicholas Matteo_, Aug 15 2019