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A093879
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First differences of A004001.
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16
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0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0
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OFFSET
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1,1
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COMMENTS
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All the terms are 0 or 1: it is easy to show that if {b(n)} = A004001, b(n)>=b(n-1) and b(n)<n, therefore the first differences form an infinite binary word. - Benoit Cloitre, Jun 05 2004
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LINKS
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R. J. Mathar, Table of n, a(n) for n = 1..9999
J. Grytczuk, Another variation on Conway's recursive sequence, Discr. Math. 282 (2004), 149-161.
D. Newman, Problem E3274, Amer. Math. Monthly, 95 (1988), 555.
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FORMULA
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From Antti Karttunen, Jan 18 2016: (Start)
a(n) = A004001(n+1) - A004001(n).
Other identities. For all n >= 1:
a(A087686(n+1)-1) = 0.
a(A088359(n)-1) = 1.
a(n) = 1 if and only if A051135(n+1) = 1.
(End)
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MATHEMATICA
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a[1] = a[2] = 1; a[n_] := a[n] = a[a[n - 1]] + a[n - a[n - 1]]; t = Table[a[n], {n, 110}]; Drop[t, 1] - Drop[t, -1] (* Robert G. Wilson v, May 28 2004 *)
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PROG
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(PARI) {m=106; v=vector(m, j, 1); for(n=3, m, a=v[v[n-1]]+v[n-v[n-1]]; v[n]=a); for(n=2, m, print1(v[n]-v[n-1], ", "))}
(Scheme) (define (A093879 n) (- (A004001 (+ 1 n)) (A004001 n))) ;; Code for A004001 given in that entry. - Antti Karttunen, Jan 18 2016
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CROSSREFS
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Cf. A004001, A051135, A087686, A088359, A188163.
Sequence in context: A108737 A165221 A295891 * A117872 A291291 A324681
Adjacent sequences: A093876 A093877 A093878 * A093880 A093881 A093882
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, May 27 2004
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EXTENSIONS
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More terms and PARI code from Klaus Brockhaus and Robert G. Wilson v, May 27 2004
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STATUS
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approved
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