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 A266205 a(n) = G_n(6), where G is the Goodstein function defined in A266201. 20
 6, 29, 257, 3125, 46655, 98039, 187243, 332147, 555551, 885775, 1357259, 2011162, 2895965, 4068068, 5592391, 7542974, 10003577, 13068280, 16842083, 21441506, 26995189, 33644492, 41544095, 50862597, 61783119, 74503901, 89238903, 106218405, 125689607, 147917229 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Nicholas Matteo, Table of n, a(n) for n = 0..10000 R. L. Goodstein, On the Restricted Ordinal Theorem, The Journal of Symbolic Logic 9, no. 2 (1944), 33-41. Wikipedia, Goodstein sequence EXAMPLE G_1(6) = B_2(6) - 1 = B_2(2^2 + 2) - 1 = 3^3 + 3 - 1 = 29; G_2(6) = B_3(G_1(6)) - 1 = B_3(3^3 + 2) - 1 =  4^4 + 2 - 1 = 257; G_3(6) = B_4(G_2(6)) - 1 = 5^5 + 1 - 1 = 3125; G_4(6) = B_5(G_3(6)) - 1 = 6^6 - 1 = 46655; 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. PROG (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 CROSSREFS 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). Sequence in context: A209112 A205811 A143563 * A321141 A122802 A144746 Adjacent sequences:  A266202 A266203 A266204 * A266206 A266207 A266208 KEYWORD nonn,fini,changed AUTHOR Natan Arie Consigli, Jan 23 2016 STATUS approved

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Last modified January 23 19:12 EST 2020. Contains 331175 sequences. (Running on oeis4.)