A266205 a(n) = G_n(6), where G is the Goodstein function defined in A266201.

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

Offset: 0

Author

Natan Arie Consigli, Jan 23 2016

Keywords

• nonn
• fini

Examples

			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.
		

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

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).

Programs

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