login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A059934 Third step in Goodstein sequences, i.e., g(5) if g(2)=n: write g(4)=A057650(n) in hereditary representation base 4, bump to base 5, then subtract 1 to produce g(5). 15
0, 2, 60, 467, 3125, 3127, 6310, 9842, 15625, 15627, 15685, 16092, 18750, 18752, 53793641718868912174424175024032593379100060 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Table of n, a(n) for n=2..16.

R. L. Goodstein, On the Restricted Ordinal Theorem, J. Symb. Logic 9, 33-41, 1944.

Eric Weisstein's World of Mathematics, Goodstein Sequence

Wikipedia, Goodstein's Theorem

Reinhard Zumkeller, Haskell programs for Goodstein sequences

EXAMPLE

a(12) = 15685 since with g(2) = 12 = 2^(2 + 1) + 2^2, we get g(3) = 3^(3 + 1) + 3^3-1 = 107 = 3^(3 + 1) + 2*3^2 + 2*3 + 2, g(4) = 4^(4 + 1) + 2*4^2 + 2*4 + 2-1 = 1065 and g(5) = 5^(5 + 1) + 2*5^2 + 2*5^1 + 1-1.

PROG

(Haskell)  see Link

CROSSREFS

Cf. A056004, A057650, A059933, A059935, A059936.

Sequence in context: A048541 A067739 A187626 * A006333 A001760 A230572

Adjacent sequences:  A059931 A059932 A059933 * A059935 A059936 A059937

KEYWORD

hard,nonn

AUTHOR

Henry Bottomley, Feb 12 2001

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 July 23 13:49 EDT 2019. Contains 325254 sequences. (Running on oeis4.)