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A307721 a(n) = x(y(n)) - y(x(n)) where x = A302128 and y = A005350. 1
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
1
COMMENTS
A chaotic sequence based on a definition by A. Fraenkel. Fibonacci numbers determine the boundaries of the generations.
LINKS
A. S. Fraenkel, Iterated floor function, algebraic numbers, discrete chaos, Beatty subsequences, semigroups, Trans. Amer. Math. Soc., Volume 341, Number 2 (1994).
Rémy Sigrist, C program for A307721
MAPLE
x:= proc(n) option remember;
procname(procname(n-2)) + procname(n-procname(n-1))
end proc:
x(1):= 1: x(2):= 1: x(3):= 1:
y:= proc(n) option remember;
procname(procname(n-1)) + procname(n-procname(n-1))
end proc:
y(1):= 1: y(2):= 1: y(3):= 1:
map(x@y-y@x, [$1..100]); # Robert Israel, Apr 25 2019
MATHEMATICA
x[1]=x[2]=x[3]=y[1]=y[2]=y[3]=1; x[n_] := x[n] = x[x[n-2]] + x[n - x[n - 1]]; y[n_] := y[n] = y[y[n-1]] + y[n - y[n-1]]; a[n_] := x[y[n]] - y[x[n]]; Array[a, 100] (* Giovanni Resta, Apr 24 2019 *)
PROG
(PARI) x=vector(200); for(n=1, 3, x[n] = 1); for(n=4, #x, x[n] = x[x[n-2]] + x[n-x[n-1]]); y=vector(200); for(n=1, 3, y[n] = 1); for(n=4, #y, y[n] = y[y[n-1]] + y[n-y[n-1]]); vector(200, n, x[y[n]]-y[x[n]])
(C) See Links section.
CROSSREFS
Sequence in context: A000004 A297046 A248805 * A023976 A025469 A025466
KEYWORD
sign
AUTHOR
Altug Alkan, Apr 24 2019
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)