

A284019


The "Hofstadter chaotic heart" sequence: a(n) = A004001(n)  A005185(n).


7



0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 2, 1, 1, 1, 0, 0, 0, 1, 2, 2, 1, 1, 1, 0, 0, 0, 4, 1, 0, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 5, 4, 4, 1, 2, 4, 0, 1, 3, 1, 1, 0, 0, 0, 0, 8, 1, 2, 4, 0, 3, 2, 2, 1, 1, 0, 2, 2, 3, 1, 4, 4, 2, 2, 4, 4, 2, 4, 3, 2
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OFFSET

1,15


COMMENTS

See also scatterplot in Links section.
From Nathan Fox, Mar 30 2017: (Start)
The pattern in the graph presumably comes from the known pattern in the Conway sequence minus n/2 (A004001) combined with the "sausage" pattern of the Qsequence (A005185). Since the Qsequence seems to remain close to n/2, the patterns combine in this way.
This means that the bottoms of the hearts should be roughly at powers of 2 and the joins between them should be where the sausages thin out. (End) [Corrected by Altug Alkan, Apr 01 2017]
Note that this comment says that the indices where the bottoms of the hearts occur (the local minima) are roughly powers of 2. For example, a(8056) = 317 is a local minimum close to 2^13.  N. J. A. Sloane, Apr 01 2017


LINKS

Altug Alkan, Table of n, a(n) for n = 1..100000
Altug Alkan, Alternative Scatterplot of A284019
Altug Alkan, Nathan Fox, and Orhan Ozgur Aybar, On Hofstadter Heart Sequences, Complexity, 2017.
Index entries for Hofstadtertype sequences


EXAMPLE

a(4) = 1 since a(4) = A004001(4)  A005185(4) = 2  3 = 1.


MAPLE

A005185:= proc(n) option remember; procname(nprocname(n1)) +procname(nprocname(n2)) end proc:
A005185(1):= 1: A005185(2):= 1:
A004001:= proc(n) option remember; procname(procname(n1)) +procname(nprocname(n1)) end proc:
A004001(1):= 1: A004001(2):= 1:
A284019:= map(A004001  A005185, [$1..1000]):
seq(A284019[i], i=1..1000); # Altug Alkan, Mar 31 2017


MATHEMATICA

a[n_] := a[n] = If[n <= 2, 1, a[a[n  1]] + a[n  a[n  1]]]; b[1] = b[2] = 1; b[n_] := b[n] = b[n  b[n  1]] + b[n  b[n  2]]; Table[a@ n  b@ n, {n, 87}] (* Michael De Vlieger, Mar 18 2017, after Robert G. Wilson v at A004001 *)


PROG

(PARI) q=vector(1000); h=vector(1000); q[1]=q[2]=1; for(n=3, #q, q[n]=q[nq[n1]]+q[nq[n2]]); h[1]=h[2]=1; for(n=3, #h, h[n]=h[h[n1]]+h[nh[n1]]); vector(1000, n, h[n]q[n])
(Scheme) (define (A284019 n) ( (A004001 n) (A005185 n))) ;; Needs also Schemecode included in those two entries.  Antti Karttunen, Mar 22 2017


CROSSREFS

Cf. A004001, A005185, A284606, A286560, A286569.
Sequence in context: A026836 A089052 A284606 * A286135 A142475 A051556
Adjacent sequences: A284016 A284017 A284018 * A284020 A284021 A284022


KEYWORD

sign,look


AUTHOR

Altug Alkan, Mar 18 2017


EXTENSIONS

Graphically descriptive name added by Antti Karttunen with permission from D. R. Hofstadter, Mar 29 2017


STATUS

approved



