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 Q-sequence (A005185). Since the Q-sequence 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.
MAPLE
A005185:= proc(n) option remember; procname(n-procname(n-1)) +procname(n-procname(n-2)) end proc:
A004001:= proc(n) option remember; procname(procname(n-1)) +procname(n-procname(n-1)) end proc:
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[n-q[n-1]]+q[n-q[n-2]]); h[1]=h[2]=1; for(n=3, #h, h[n]=h[h[n-1]]+h[n-h[n-1]]); vector(1000, n, h[n]-q[n])
(Scheme) (define (A284019 n) (- (A004001 n) (A005185 n))) ;; Needs also Scheme-code included in those two entries. - Antti Karttunen, Mar 22 2017
CROSSREFS
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