A093879 First differences of A004001.

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

Offset

1,1

Comments

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

Links

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.

Formula

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)

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A004001, A051135, A087686, A088359, A188163.

Sequence in context: A108737 A165221 A295891 * A117872 A291291 A324681

Adjacent sequences: A093876 A093877 A093878 * A093880 A093881 A093882

Keyword

nonn,easy

Author

N. J. A. Sloane, May 27 2004

Extensions

More terms and PARI code from Klaus Brockhaus and Robert G. Wilson v, May 27 2004

Status

approved