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%I #20 Apr 24 2024 12:37:40
%S 1,83,775,46655,46657,93395,140743,279935,279937,280019,280711,326591,
%T 326593,
%U 19916489515870532960258562190639398471599239042185934648024761145811
%N Fourth step in Goodstein sequences, i.e., g(6) if g(2)=n: write g(5)=A059934(n) in hereditary representation base 5, bump to base 6, then subtract 1 to produce g(6).
%C 2.659...*10^36305 = a(18) < a(19) < ... < a(31) = a(18) + 326594. - _Pontus von Brömssen_, Sep 20 2020
%H Pontus von Brömssen, <a href="/A059935/b059935.txt">Table of n, a(n) for n = 3..17</a>
%H R. L. Goodstein, <a href="http://www.jstor.org/stable/2268019">On the Restricted Ordinal Theorem</a>, J. Symb. Logic 9, 33-41, 1944.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoodsteinSequence.html">Goodstein Sequence</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Goodstein's_theorem">Goodstein's Theorem</a>
%H Reinhard Zumkeller, <a href="/A211378/a211378.hs.txt">Haskell programs for Goodstein sequences</a>
%e a(12) = 280019 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 and g(6) = 6^(6 + 1) + 2*6^2 + 6 + 5 = 280019.
%o (Haskell) -- See Link
%o (Python)
%o from sympy.ntheory.factor_ import digits
%o def bump(n,b):
%o s=digits(n,b)[1:]
%o l=len(s)
%o return sum(s[i]*(b+1)**bump(l-i-1,b) for i in range(l) if s[i])
%o def A059935(n):
%o for i in range(2,6):
%o n=bump(n,i)-1
%o return n # _Pontus von Brömssen_, Sep 20 2020
%Y Cf. A056004, A057650, A059933, A059934, A059936.
%K nonn,changed
%O 3,2
%A _Henry Bottomley_, Feb 12 2001
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