A271986 G_10(n), where G is the Goodstein function defined in A266201.

0, 299, 5643, 1357259, 273624711, 17832200896811, 26748301350411, 44580503598539, 62412976762503, 106993205379371, 106993205384715, 106993206736331, 106993479003783

Offset: 3

Author

Natan Arie Consigli, May 01 2016

Keywords

• nonn

Comments

a(17) = 1.926...*10^6103. - Pontus von Brömssen, Sep 25 2020

Links

• Pontus von Brömssen, Table of n, a(n) for n = 3..16
• Wikipedia, Goodstein's theorem

Crossrefs

Cf. A056004: G_1(n); A057650: G_2(n); A059934: G_3(n); A059935: G_4(n); A059936: G_5(n); A271977: G_6(n); A271978: G_7(n); A271979: G_8(n); A271985: G_9(n); this sequence: G_10(n); A266201: G_n(n).

Programs

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 A271986(n):
  if n==3: return 0
  for i in range(2,12):
    n=bump(n,i)-1
  return n # Pontus von Brömssen, Sep 25 2020

Extensions

Incorrect program and terms removed by Pontus von Brömssen, Sep 25 2020