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

%I A271977 #23 Sep 25 2020 09:26:00
%S A271977 0,139,1751,187243,16777215,33554571,50333399,84073323,134217727,
%T A271977 134217867,134219479,134404971,150994943
%N A271977 G_6(n), where G is the Goodstein function defined in A266201.
%C A271977 The next term (line break for better formatting) is a(16) = \
%C A271977 1619239197880733074062994004113160848331305687934176134326809 \
%C A271977 538279709713884753268291640071900343455846003089194770060104834018705547.
%C A271977 a(17) = 2.870...*10^1585, a(18) = 6.943...*10^169099. - _Pontus von Brömssen_, Sep 24 2020
%H A271977 Pontus von Brömssen, <a href="/A271977/b271977.txt">Table of n, a(n) for n = 3..16</a>
%H A271977 Wikipedia, <a href="https://en.wikipedia.org/wiki/Goodstein&#39;s_theorem">Goodstein's theorem</a>
%e A271977 Find G_6(7):
%e A271977 G_1(7) = B_2(7)-1= B_2(2^2+2+1)-1 = 3^3+3+1-1 = 30;
%e A271977 G_2(7) = B_3(G_1(7))-1 = B_3(3^3+3)-1 =  4^4+4-1 = 259;
%e A271977 G_3(7) = B_4(G_2(7))-1 = 5^5+3-1 = 3127;
%e A271977 G_4(7) = B_5(G_3(7))-1 = 6^6+2-1 = 46657;
%e A271977 G_5(7) = B_6(G_4(7))-1 = 7^7+1-1 = 823543;
%e A271977 G_6(7) = B_7(G_5(7))-1 = 8^8-1 = 16777215.
%o A271977 (Python)
%o A271977 from sympy.ntheory.factor_ import digits
%o A271977 def bump(n,b):
%o A271977   s=digits(n,b)[1:]
%o A271977   l=len(s)
%o A271977   return sum(s[i]*(b+1)**bump(l-i-1,b) for i in range(l) if s[i])
%o A271977 def A271977(n):
%o A271977   if n==3: return 0
%o A271977   for i in range(2,8):
%o A271977     n=bump(n,i)-1
%o A271977   return n # _Pontus von Brömssen_, Sep 24 2020
%Y A271977 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).
%K A271977 nonn
%O A271977 3,2
%A A271977 _Natan Arie Consigli_, Apr 24 2016
%E A271977 a(10) corrected by _Pontus von Brömssen_, Sep 24 2020