

A087777


a(1) = ... = a(4) = 1; a(n) = a(n  a(n2)) + a(n  a(n4)).


6



1, 1, 1, 1, 2, 4, 6, 7, 7, 5, 3, 8, 9, 11, 12, 9, 9, 13, 11, 9, 13, 16, 13, 19, 16, 11, 14, 16, 21, 22, 14, 14, 19, 17, 22, 27, 25, 16, 20, 28, 22, 22, 26, 25, 24, 32, 26, 22, 29, 29, 32, 35, 32, 27, 26, 34, 30, 33, 40, 25, 27, 46, 40, 33, 32, 28, 36, 50, 44, 31, 36, 38, 46, 53, 41, 29, 41
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,5


COMMENTS

This is the sequence Q(2,4) in the HofstadterHuber classification.
It is not known if this sequence is defined for all positive n. Balamohan et al. comment that it shows "inscrutably wild behavior".


LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..10000
B. Balamohan, A. Kuznetsov and S. Tanny, On the behavior of a variant of Hofstadter's Qsequence, J. Integer Sequences, Vol. 10 (2007), #07.7.1.
Nathan Fox, A Slow Relative of Hofstadter's QSequence, arXiv:1611.08244 [math.NT], 2016.
D. R. Hofstadter, Curious patterns and nonpatterns in a family of metaFibonacci recursions, Lecture in Doron Zeilberger's Experimental Mathematics Seminar, Rutgers University, April 10 2014; Part 1, Part 2.
D. R. Hofstadter, Plot of first 100000 terms
Index entries for Hofstadtertype sequences


MAPLE

a := proc(n) option remember; if n<=4 then 1 else if n > a(n2) and n > a(n4) then RETURN(a(na(n2))+a(na(n4))); else ERROR(" died at n= ", n); fi; fi; end;


MATHEMATICA

a[n_] := a[n] = If[n <= 4, 1, a[n  a[n  2]] + a[n  a[n  4]]];
Array[a, 80] (* JeanFrançois Alcover, Nov 24 2017 *)


PROG

(MAGMA) [n le 4 select 1 else Self(nSelf(n2))+Self(nSelf(n4)): n in [1..80]]; // Vincenzo Librandi, Sep 10 2016


CROSSREFS

Cf. A005185 (Q(1,2)), A063882 (Q(1,4)), A046700.
Sequence in context: A114431 A167689 A058184 * A030118 A023835 A272633
Adjacent sequences: A087774 A087775 A087776 * A087778 A087779 A087780


KEYWORD

nonn


AUTHOR

Roger L. Bagula, Oct 05 2003


EXTENSIONS

Edited by N. J. A. Sloane, Nov 06 2007


STATUS

approved



