A271977 G_6(n), where G is the Goodstein function defined in A266201.

0, 139, 1751, 187243, 16777215, 33554571, 50333399, 84073323, 134217727, 134217867, 134219479, 134404971, 150994943

Offset

3,2

Comments

The next term (line break for better formatting) is a(16) = \

1619239197880733074062994004113160848331305687934176134326809 \

538279709713884753268291640071900343455846003089194770060104834018705547.

a(17) = 2.870...*10^1585, a(18) = 6.943...*10^169099. - Pontus von Brömssen, Sep 24 2020

Links

Pontus von Brömssen, Table of n, a(n) for n = 3..16

Wikipedia, Goodstein's theorem

Example

Find G_6(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.

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 A271977(n):
  if n==3: return 0
  for i in range(2, 8):
    n=bump(n, i)-1
  return n # Pontus von Brömssen, Sep 24 2020

Crossrefs

Cf. A056004: G_1(n); A057650: G_2(n); A059934: G_3(n); A059935: G_4(n); A059936: G_5(n); this sequence: G_6(n); A271978: G_7(n); A271979: G_8(n); A271985: G_9(n); A271986: G_10(n); A266201: G_n(n).

Sequence in context: A377295 A358400 A175017 * A217724 A230693 A223163

Adjacent sequences: A271974 A271975 A271976 * A271978 A271979 A271980

Keyword

nonn

Author

Natan Arie Consigli, Apr 24 2016

Extensions

a(10) corrected by Pontus von Brömssen, Sep 24 2020

Status

approved