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A215409
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The Goodstein sequence G(3).
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4
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OFFSET
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1,1
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COMMENTS
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The first term in the Goodstein sequence G(m) is m itself. To get the 2nd term, write m in hereditary base 2 notation (see links), change all the 2s to 3s, and then subtract 1 from the result. To get the 3rd term, write the 2nd term in hereditary base 3 notation, change all 3s to 4s, and subtract 1 again. Continue until the result is zero (by Goodstein's Theorem), when the sequence terminates.
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REFERENCES
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R. Goodstein, On the restricted ordinal theorem, J. Symbolic Logic 9 (1944), 33-41.
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LINKS
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Table of n, a(n) for n=1..6.
Eric Weisstein's World of Mathematics, Hereditary Representation
Eric Weisstein's World of Mathematics, Goodstein Sequence
Eric Weisstein's World of Mathematics, Goodstein's Theorem
Wikipedia, Hereditary base-n notation
Wikipedia, Goodstein sequence
Wikipedia, Goodstein's Theorem
_Reinhard Zumkeller_, Haskell programs for Goodstein sequences
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EXAMPLE
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a(1) = 3 = 2^1 + 1; a(2) = 3^1 + 1 - 1 = 3^1 = 3; a(3) = 4^1 - 1 = 3; a(4) = 3 - 1 = 2; a(5) = 2 - 1 = 1; a(6) = 1 - 1 = 0.
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PROG
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(Haskell) see Link
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CROSSREFS
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Cf. A056004, A056041, A056193, A057650, A059933, A059934, A059935, A059936.
Sequence in context: A076237 A201432 A128210 * A153012 A016651 A135877
Adjacent sequences: A215406 A215407 A215408 * A215410 A215411 A215412
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KEYWORD
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nonn,fini,full
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AUTHOR
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Jonathan Sondow, Aug 10 2012
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STATUS
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approved
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