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A056004 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. 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

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.

LINKS

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

EXAMPLE

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

PROG

(Haskell)  see Link

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Henry Bottomley, Aug 04 2000

STATUS

approved

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Last modified July 28 12:23 EDT 2014. Contains 244997 sequences.