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

Author

N. J. A. Sloane, May 27 2004

Keywords

• nonn
• easy

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)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.

Crossrefs

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

Programs

Magma

h:=[n le 2 select 1 else Self(Self(n-1)) + Self(n-Self(n-1)): n in [1..160]];
A093879:= func< n | h[n+1] - h[n] >;
[A093879(n): n in [1..120]]; // G. C. Greubel, May 19 2024

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 *)

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],","))}

SageMath

@CachedFunction
def h(n): return 1 if (n<3) else h(h(n-1)) + h(n - h(n-1))
def A093879(n): return h(n+1) - h(n)
[A093879(n) for n in range(1,101)] # G. C. Greubel, May 19 2024

Scheme

(define (A093879 n) (- (A004001 (+ 1 n)) (A004001 n))) ;; Code for A004001 given in that entry. - Antti Karttunen, Jan 18 2016

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)

Extensions

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