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A059936
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Fifth step in Goodstein sequences, i.e., g(7) if g(2)=n: write g(6)=A059935(n) in hereditary representation base 6, bump to base 7, then subtract 1 to produce g(7).
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19
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0, 109, 1197, 98039, 823543, 1647195, 2471826, 4215754, 5764801, 5764910, 5765998, 5862840, 6588344, 5103708485122940631839901111036829791435007685667303872450435153015345686896530517814322070729709
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OFFSET
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3,2
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COMMENTS
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a(17) = 4.587...*10^1014, a(18) = 1.505...*10^82854, and 3.759...*10^695974 = a(19) < a(20) < ... < a(31) = a(19) + 6588344. - Pontus von Brömssen, Sep 20 2020
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LINKS
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EXAMPLE
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a(12) = 5764910 since with g(2) = 12 = 2^(2 + 1) + 2^2, we get g(3) = 3^(3 + 1) + 3^3-1 = 107 = 3^(3 + 1) + 2*3^2 + 2*3 + 2, g(4) = 4^(4 + 1) + 2*4^2 + 2*4 + 1 = 1065, g(5) = 5^(5 + 1) + 2*5^2 + 2*5 = 15685, g(6) = 6^(6 + 1) + 2*6^2 + 6 + 5 = 280019 and g(7) = 7^(7 + 1) + 2*7^2 + 7 + 4 = 5764910.
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PROG
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(Haskell) see Link
(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])
for i in range(2, 7):
n=bump(n, i)-1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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