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A057650 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). 9
1, 3, 41, 255, 257, 259, 553, 1023, 1025, 1027, 1065, 1279, 1281, 1283, 50973998591214355139406377, 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084095 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

REFERENCES

Goodstein, R. L. "On the Restricted Ordinal Theorem." J. Symb. Logic 9, 33-41, 1944.

LINKS

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

EXAMPLE

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.

PROG

(Haskell)  see Link

CROSSREFS

Cf. A056004, A059933, A059934, A059935, A059936.

Sequence in context: A229080 A106978 A089131 * A181226 A159249 A087544

Adjacent sequences:  A057647 A057648 A057649 * A057651 A057652 A057653

KEYWORD

nonn

AUTHOR

Henry Bottomley, Oct 13 2000

STATUS

approved

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Last modified November 27 13:25 EST 2014. Contains 250196 sequences.