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 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 (list; graph; refs; listen; history; text; internal format)
 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. EXAMPLE a(4) = -1 since a(4) = A004001(4) - A005185(4) = 2 - 3 = -1. MAPLE A005185:= proc(n) option remember; procname(n-procname(n-1)) +procname(n-procname(n-2)) end proc: A005185(1):= 1: A005185(2):= 1: A004001:= proc(n) option remember; procname(procname(n-1)) +procname(n-procname(n-1)) 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[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 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

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Last modified October 26 08:06 EDT 2020. Contains 338027 sequences. (Running on oeis4.)