OFFSET
3,2
COMMENTS
2.659...*10^36305 = a(18) < a(19) < ... < a(31) = a(18) + 326594. - Pontus von Brömssen, Sep 20 2020
LINKS
Pontus von Brömssen, Table of n, a(n) for n = 3..17
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) = 280019 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 + 1 = 1065, g(5) = 5^(5 + 1) + 2*5^2 + 2*5 = 15685 and g(6) = 6^(6 + 1) + 2*6^2 + 6 + 5 = 280019.
PROG
(Haskell) -- See Link
(Python)
from sympy.ntheory.factor_ import digits
def bump(n, b):
s=digits(n, b)[1:]
l=len(s)
return sum(s[i]*(b+1)**bump(l-i-1, b) for i in range(l) if s[i])
def A059935(n):
for i in range(2, 6):
n=bump(n, i)-1
return n # Pontus von Brömssen, Sep 20 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Feb 12 2001
STATUS
approved