The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A005229 a(1) = a(2) = 1; for n > 2, a(n) = a(a(n-2)) + a(n - a(n-2)). (Formerly M0441) 40
 1, 1, 2, 3, 3, 4, 5, 6, 6, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 21, 22, 23, 24, 24, 25, 26, 26, 27, 28, 29, 29, 30, 30, 30, 31, 32, 33, 34, 35, 36, 36, 37, 37, 38, 39, 39, 40, 41, 42, 43, 43, 44, 45, 45, 45, 46 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS By induction a(n) <= n, but an exact rate of growth is not known. REFERENCES J. Arkin, D. C. Arney, L. S. Dewald, and W. E. Ebel, Jr., Families of recursive sequences, J. Rec. Math., 22 (No. 22, 1990), 85-94. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n=1..1000 Altug Alkan, On a Generalization of Hofstadter's Q-Sequence: A Family of Chaotic Generational Structures, Complexity (2018), Article ID 8517125. Nick Hobson, Python program for this sequence C. L. Mallows, Conway's challenge sequence, Amer. Math. Monthly, 98 (1991), 5-20. N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98). Eric Weisstein's World of Mathematics, Mallows' Sequence. MAPLE A005229:= proc(n) option remember; if n<=2 then 1 else A005229(A005229(n-2)) +A005229(n-A005229(n-2)); fi; end; seq(A005229(n), n=1..70) MATHEMATICA a[1] = a[2] = 1; a[n_] := a[n] = a[a[n-2]] + a[n - a[n-2]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Sep 06 2013 *) PROG (PARI) a(n)=an[n]; an=vector(100, n, 1); for(n=3, 100, an[n]=a(a(n-2))+a(n-a(n-2))) (Haskell) import Data.Function (on) a005229 n = a005229_list !! (n-1) a005229_list = 1 : 1 : zipWith ((+) `on` a005229) a005229_list (zipWith (-) [3..] a005229_list) -- Reinhard Zumkeller, Jan 17 2014 (Sage) @CachedFunction def a(n): # A005229 if (n<3): return 1 else: return a(a(n-2)) + a(n-a(n-2)) [a(n) for n in (1..100)] # G. C. Greubel, Mar 27 2022 CROSSREFS Cf. A004001, A051105, A087758, A116591, A147880, A169638. Sequence in context: A132351 A025556 A338006 * A091245 A347649 A100618 Adjacent sequences: A005226 A005227 A005228 * A005230 A005231 A005232 KEYWORD nonn,nice,easy AUTHOR EXTENSIONS Typo in definition corrected by Nick Hobson, Feb 21 2007 STATUS approved

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

Last modified November 26 20:01 EST 2022. Contains 358362 sequences. (Running on oeis4.)