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A271985 G_9(n), where G is the Goodstein function defined in A266201. 6
0, 253, 4382, 885775, 150051213, 570623341475, 855935016215, 1426559238830, 1997331745490, 3138428376974, 3138428381103, 3138429262496, 3138578427934 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

COMMENTS

a(17) = 2.066...*10^4574. - Pontus von Brömssen, Sep 25 2020

LINKS

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

Wikipedia, Goodstein's theorem

EXAMPLE

Compute G_9(10):

G_1(10)= B_2(10)-1 = B_2(2^(2+1)+2)-1 = 3^(3+1)+3-1 = 83;

G_2(10) = B_3(3^(3+1)+2)-1 = 4^(4+1)+2-1 = 1025;

G_3(10) = B_4(4^(4+1)+1)-1 = 5^(5+1)+1-1 = 15625;

G_4(10) = B_5(5*5^(5+1))-1 = 6^(6+1)-1= 279935;

G_5(10) = B_6(5*6^6+5*6^5+5*6^4+5*6^3+5*6^2+5*6+5)-1 = 5*7^7+5*7^5+5*7^4+5*7^3+5*7^2+5*7+5-1 = 4215754;

G_6(10) = B_7(5*7^7+5*7^5+5*7^4+5*7^3+5*7^2+5*7+4)-1 = 5*8^8+5*8^5+5*8^4+5*8^3+5*8^2+5*8+4-1 = 84073323;

G_7(10) = B_8(5*8^8+5*8^5+5*8^4+5*8^3+5*8^2+5*8+3)-1 = 5*9^9+5*9^5+5*9^4+5*9^3+5*9^2+5*9+3-1 = 1937434592;

G_8(10) = B_9(5*9^9+5*9^5+5*9^4+5*9^3+5*9^2+5*9+2)-1 = 5*10^10+5*10^5+5*10^4+5*10^3+5*10^2+5*10+2-1 = 50000555551;

G_9(10) = B_10(5*10^10+5*10^5+5*10^4+5*10^3+5*10^2+5*10+1)-1 = 5*11^11+5*11^5+5*11^4+5*11^3+5*11^2+5*11+1-1 = 1426559238830.

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 A271985(n):

  if n==3: return 0

  for i in range(2, 11):

    n=bump(n, i)-1

  return n # Pontus von Brömssen, Sep 25 2020

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); this sequence: G_9(n); A271986: G_10(n); A266201: G_n(n).

Sequence in context: A183449 A225021 A242463 * A255182 A176087 A006060

Adjacent sequences:  A271982 A271983 A271984 * A271986 A271987 A271988

KEYWORD

nonn

AUTHOR

Natan Arie Consigli, Apr 30 2016

EXTENSIONS

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

STATUS

approved

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Last modified February 24 12:52 EST 2021. Contains 341569 sequences. (Running on oeis4.)