A211378 Goodstein sequence starting with 19.

19, 7625597484990, 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084099

Offset

0,1

Comments

To calculate a(n), write a(n-1) in the hereditary representation base n+1, then bump the base to n+2, then subtract 1.

Links

Table of n, a(n) for n=0..2.

Eric Weisstein's World of Mathematics, Goodstein Sequence

Wikipedia, Goodstein's Theorem

Reinhard Zumkeller, Haskell programs for Goodstein sequences

Example

The first terms are (see Wikipedia):
a(0) = 2^2^2 + 2^1 + 2^0 = 19
a(1) = 3^3^3 + 3^1 + 3^0 - 1 = 7625597484990
a(2) = 4^4^4 + 4^1 - 1                       (155 digits)
a(3) = 5^5^5 + 3 - 1                         (2185 digits)
a(4) = 6^6^6 + 2 - 1                         (36306 digits)
a(5) = 7^7^7 + 1 - 1                         (695975 digits)
a(6) = 8^8^8 - 1                             (15151336 digits).

Prog

(Haskell)  see Link

Crossrefs

Cf. A215409 (start=3), A056193 (start=4), A222117 (start=15), A059933 (start=16).

Sequence in context: A013890 A347353 A128400 * A133591 A137643 A351570

Adjacent sequences: A211375 A211376 A211377 * A211379 A211380 A211381

Keyword

nonn,fini

Author

Reinhard Zumkeller, Feb 13 2013

Extensions

Offset changed to 0 by Nicholas Matteo, Aug 21 2019

Status

approved