login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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