OFFSET
3,2
COMMENTS
a(16) is too big to include - see b-file. a(17) = 9.221...*10^2347, a(18) = 2.509...*10^316952. - Pontus von Brömssen, Sep 25 2020
LINKS
Pontus von Brömssen, Table of n, a(n) for n = 3..16
Wikipedia, Goodstein's theorem
EXAMPLE
Find G_7(7):
G_1(7) = B_2(7)-1= B[2](2^2+2+1)-1 = 3^3+3+1-1 = 30;
G_2(7) = B_3(G_1(7))-1 = B[3](3^3+3)-1 = 4^4+4-1 = 259;
G_3(7) = B_4(G_2(7))-1 = 5^5+3-1 = 3127;
G_4(7) = B_5(G_3(7))-1 = 6^6+2-1 = 46657;
G_5(7) = B_6(G_4(7))-1 = 7^7+1-1 = 823543;
G_6(7) = B_7(G_5(7))-1 = 8^8-1 = 16777215;
G_7(7) = B_8(G_6(7))-1 = 7*9^7+7*9^6+7*9^5+7*9^4+7*9^3+7*9^2+7*9+7-1 = 37665879.
PROG
(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 A271978(n):
if n==3: return 0
for i in range(2, 9):
n=bump(n, i)-1
return n # Pontus von Brömssen, Sep 25 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Natan Arie Consigli, Apr 30 2016
EXTENSIONS
a(9) corrected by Pontus von Brömssen, Sep 25 2020
STATUS
approved