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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). 18
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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 2..1000

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

Eric Weisstein's World of Mathematics, Hereditary 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: A106978 A260832 A089131 * A280176 A322244 A181226

Adjacent sequences:  A057647 A057648 A057649 * A057651 A057652 A057653

KEYWORD

nonn

AUTHOR

Henry Bottomley, Oct 13 2000

STATUS

approved

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Last modified December 5 16:22 EST 2020. Contains 338954 sequences. (Running on oeis4.)