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A266204 a(n) = G_n(5), where G_n(k) is the Goodstein function defined in A266201.

%I A266204 #37 Jan 11 2020 15:57:47
%S A266204 5,27,255,467,775,1197,1751,2454,3325,4382,5643,7126,8849,10830,13087,
%T A266204 15637,18499,21691,25231,29137,33427,38119,43231,48781,54787,61267,
%U A266204 68239,75721,83731,92287,101407,111108,121409,132328,143883,156092,168973,182544,196823
%N A266204 a(n) = G_n(5), where G_n(k) is the Goodstein function defined in A266201.
%H A266204 Nicholas Matteo, <a href="/A266204/b266204.txt">Table of n, a(n) for n = 0..10000</a>
%H A266204 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 A266204 Wikipedia, <a href="http://en.wikipedia.org/wiki/Goodstein%27s_theorem#Goodstein_sequences">Goodstein sequence</a>
%e A266204 G_0(5) = 5;
%e A266204 G_1(5) = B_2(5) - 1 = B_2(2^2 + 1) - 1 = 27;
%e A266204 G_2(5) = B_3(3^3) - 1 = 4^4 - 1 = 255;
%e A266204 G_3(5) = B_4(3*4^3 + 3*4^2 + 3*4 + 3) - 1 = 3*5^3 + 3*5^2 + 3*5 + 3 - 1 = 467.
%o A266204 (PARI) bump(a, n) = {if (a < n, return (a)); my(pd = Pol(digits(a, n)));  my(de = vector(poldegree(pd)+1, k, k--; polcoeff(pd, k))); my(bde = vector(#de, k, k--; bump(k, n))); my(q = sum(k=0, poldegree(pd), if (c=polcoeff(pd, k), c*x^bde[k+1], 0))); return(subst(q, x, n+1)); }
%o A266204 lista(nn) = {print1(a = 5, ", "); for (n=2, nn, a = bump(a, n)-1; print1(a, ", "); ); } \\ _Michel Marcus_, Feb 28 2016
%Y A266204 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 A266204 nonn,fini
%O A266204 0,1
%A A266204 _Natan Arie Consigli_, Jan 22 2016