OFFSET
1,1
COMMENTS
Compare to A222117: the underlying variants to define Goodstein sequences are equivalent.
REFERENCES
Helmut Schwichtenberg and Stanley S. Wainer, Proofs and Computations, Cambridge University Press, 2012; 4.4.1, page 148ff.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..250
R. L. Goodstein, On the Restricted Ordinal Theorem, The Journal of Symbolic Logic, Vol. 9, No. 2, Jun., 1944.
Wikipedia, Goodstein's Theorem
Reinhard Zumkeller, Haskell programs for Goodstein sequences
EXAMPLE
a(1) - 1 = 15 = 2^3 + 2^2 + 2^1 + 2^0 = 2^(2^1+1) + 2^2 + 2^1 + 2^0
-> a(2) = 3^(3^1+1) + 3^3 + 3^1 + 3^0 = 112;
a(2) - 1 = 111 = 3^(3^1+1) + 3^3 + 3^1
-> a(3) = 4^(4^1+1) + 4^4 + 4^1 = 1284;
a(3) - 1 = 1283 = 4^(4^1+1) + 4^4 + 3*4^0
-> a(4) = 5^(5^1+1) + 5^5 + 3*5^0 = 18753;
a(4) - 1 = 18752 = 5^(5^1+1) + 5^5 + 2*5^0
-> a(5) = 6^(6^1+1) + 6^6 + 2*6^0 = 326594;
a(5) - 1 = 326593 = 6^(6^1+1) + 6^6 + 6^0
-> a(6) = 7^(7^1+1) + 7^7 + 7^0 = 6588345.
PROG
(Haskell) -- See Link
CROSSREFS
KEYWORD
nonn,fini
AUTHOR
Reinhard Zumkeller, Feb 13 2013
STATUS
approved