The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A056004 Initial step in Goodstein sequences: write n in hereditary representation base 2, bump to base 3, then subtract 1. 21
 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 COMMENTS To write an integer n in base-k hereditary representation, write n in ordinary base-k representation, and then do the same recursively for all exponents which are greater than k: e.g., 2^18 = 2^(2^4 + 2) = 2^(2^(2^2) + 2). "Bump to base 3" means to replace all the 2's in that representation by 3. - M. F. Hasler, Feb 19 2017 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 A. E. Caicedo, Goodstein's function, Revista Colombiana de Matemáticas 41 (2007), 381-391. R. L. Goodstein, On the Restricted Ordinal Theorem, J. Symb. Logic 9, 33-41, 1944. L. Kirby, and J. Paris, Accessible independence results for Peano arithmetic, Bull. London Mathematical Society, 14 (1982), 285-293. 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 (PARI) A056004(n)=sum(i=1, #n=binary(n), if(n[i], 3^if(#n-i<2, #n-i, A056004(#n-i)+1)))-1 \\ See A266201 for more general code. - M. F. Hasler, Feb 19 2017 CROSSREFS Using G_k to denote the k-th step, this is the first in the following list: A056004: G_1(n), A057650: G_2(n), A059934: G_3(n), A059935: G_4(n), A059936: G_5(n); A266201: G_n(n); A056041. Cf. A215409: G_n(3), A056193: G_n(4), A266204: G_n(5), A266205: G_n(6), A222117: G_n(15), A059933: G_n(16), A211378: G_n(19). See A222112 for an alternate version. 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 EXTENSIONS Edited by M. F. Hasler, Feb 19 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 9 19:46 EDT 2020. Contains 335545 sequences. (Running on oeis4.)