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A059934
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Third step in Goodstein sequences, i.e., g(5) if g(2)=n: write g(4)=A057650(n) in hereditary representation base 4, bump to base 5, then subtract 1 to produce g(5).
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16
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0, 2, 60, 467, 3125, 3127, 6310, 9842, 15625, 15627, 15685, 16092, 18750, 18752, 53793641718868912174424175024032593379100060
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OFFSET
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2,2
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COMMENTS
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1.911...*10^2184 = a(18) < a(19) < ... < a(31) = a(18) + 18752. - Pontus von Brömssen, Sep 20 2020
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LINKS
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EXAMPLE
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a(12) = 15685 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 + 2-1 = 1065 and g(5) = 5^(5 + 1) + 2*5^2 + 2*5^1 + 1-1.
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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, 5):
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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STATUS
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approved
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