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A057650
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Second step in Goodstein sequences, i.e. g(4) if g(2)=n: (first step) write g(2)=n in hereditary representation base 2, bump to base 3, then subtract 1 to produce g(3)=A056004(n), then (second step) write g(3) in hereditary representation base 3, bump to base 4, then subtract 1 to produce g(4).
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8
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1, 3, 41, 255, 257, 259, 553, 1023, 1025, 1027, 1065, 1279, 1281, 1283, 50973998591214355139406377, 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084095
(list;
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refs;
listen;
history;
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internal format)
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OFFSET
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2,2
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REFERENCES
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Goodstein, R. L. "On the Restricted Ordinal Theorem." J. Symb. Logic 9, 33-41, 1944.
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 2..1000
Eric Weisstein's World of Mathematics, Heriditary Representation.
Eric Weisstein's World of Mathematics, Goodstein Sequence.
Wikipedia, Goodstein's Theorem
_Reinhard Zumkeller_, Haskell programs for Goodstein sequences
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EXAMPLE
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a(12)=1065 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 and g(4)=4^(4+1)+2*4^2+2*4+2-1=1065. a(17)=4^(4^4)-1, with g(2)=17=2^(2^2)+1 and g(3)=3^(3^3). Similarly a(18)=4^(4^4)+1, with g(2)=18=2^(2^2)+2 and g(3)=3^(3^3)+2.
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PROG
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(Haskell) see Link
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CROSSREFS
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Cf. A056004, A059933, A059934, A059935, A059936.
Sequence in context: A080347 A106978 A089131 * A181226 A159249 A087544
Adjacent sequences: A057647 A057648 A057649 * A057651 A057652 A057653
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley, Oct 13 2000
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STATUS
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approved
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