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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 December 2 19:54 EST 2023. Contains 367526 sequences. (Running on oeis4.)