

A215409


The Goodstein sequence G(3).


5




OFFSET

1,1


COMMENTS

The first term in the Goodstein sequence G(m) is m itself. To get the 2nd term, write m in hereditary base 2 notation (see links), change all the 2s to 3s, and then subtract 1 from the result. To get the 3rd term, write the 2nd term in hereditary base 3 notation, change all 3s to 4s, and subtract 1 again. Continue until the result is zero (by Goodstein's Theorem), when the sequence terminates.


REFERENCES

R. Goodstein, On the restricted ordinal theorem, J. Symbolic Logic 9 (1944), 3341.


LINKS

Table of n, a(n) for n=1..6.
Eric Weisstein's World of Mathematics, Hereditary Representation
Eric Weisstein's World of Mathematics, Goodstein Sequence
Eric Weisstein's World of Mathematics, Goodstein's Theorem
Wikipedia, Hereditary basen notation
Wikipedia, Goodstein sequence
Wikipedia, Goodstein's Theorem
Reinhard Zumkeller, Haskell programs for Goodstein sequences


EXAMPLE

a(1) = 3 = 2^1 + 1; a(2) = 3^1 + 1  1 = 3^1 = 3; a(3) = 4^1  1 = 3; a(4) = 3  1 = 2; a(5) = 2  1 = 1; a(6) = 1  1 = 0.


PROG

(Haskell) see Link


CROSSREFS

Cf. A056004, A056041, A056193, A057650, A059933, A059934, A059935, A059936.
Sequence in context: A076237 A201432 A128210 * A239232 A153012 A016651
Adjacent sequences: A215406 A215407 A215408 * A215410 A215411 A215412


KEYWORD

nonn,fini,full


AUTHOR

Jonathan Sondow, Aug 10 2012


STATUS

approved



