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A056004
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Initial step in Goodstein sequences, i.e. g(3) if g(2)=n: write n in hereditary representation base 2, bump to base 3, then subtract 1.
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11
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0, 2, 3, 26, 27, 29, 30, 80, 81, 83, 84, 107, 108, 110, 111, 7625597484986, 7625597484987, 7625597484989, 7625597484990, 7625597485013, 7625597485014, 7625597485016, 7625597485017, 7625597485067, 7625597485068, 7625597485070
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history;
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OFFSET
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1,2
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REFERENCES
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A. E. Caicedo, Goodstein's function, Revista Colombiana de Matemáticas 41 (2007), 381-391.
Goodstein, R., On the restricted ordinal theorem, J. Symbolic Logic, 9 (1944), 33-41.
Kirby, L. and Paris, J., Accessible independence results for Peano arithmetic, Bull. London Mathematical Society, 14 (1982), 285-293.
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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(18)=7625597484989 since 18=2^(2^2)+2^1 which when bumped from 2 to 3 becomes 3^(3^3)+3^1=76255974849890 and when 1 is subtracted gives 7625597484989
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PROG
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(Haskell) see Link
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CROSSREFS
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Cf. A056041 A056004 A059934 A057650 A056193 A059933 A059935 A059936 A215409.
See A222112 for a comparable definition.
Sequence in context: A060371 A130975 A002748 * A032812 A099006 A041659
Adjacent sequences: A056001 A056002 A056003 * A056005 A056006 A056007
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley, Aug 04 2000
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STATUS
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approved
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