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

0,1

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 * A344434 A321141 A359053

Adjacent sequences: A266202 A266203 A266204 * A266206 A266207 A266208

Keyword

nonn,fini

Author

Natan Arie Consigli, Jan 23 2016

Status

approved