A269162 - OEIS

%I #20 Feb 23 2016 03:43:22

%S 0,0,0,0,0,0,0,1,0,0,0,0,0,3,2,0,0,0,0,0,0,0,0,0,0,7,6,5,4,0,0,0,0,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,15,14,13,12,11,10,0,8,0,0,0,0,0,0,9,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,31,30,29,28,27,26,0,24,23,22,21,20,0,0,25

%N a(0) = 0, for n > 0, a(n) = the least (necessarily also unique) k such that A269160(k) = n, or 0 if no such k exists.

%C If n > 0 and a(n) > 0 then a(n) is the unique finite predecessor of the configuration encoded in the binary representation of n (A007088) when Wolfram's Rule 30 cellular automaton is applied.

%H Antti Karttunen, <a href="/A269162/b269162.txt">Table of n, a(n) for n = 0..16387</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rule30.html">Rule 30</a>

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>

%F Other identities. For all n >= 0:

%F a(A269160(n)) = n. [This sequence works as a left inverse of A269160.]

%F a(A110240(n+1)) = A110240(n).

%t (* empirical *) a[n_] := Module[{k}, For[k = Floor[n/7], k <= Ceiling[n/3], k++, If[BitXor[k, BitOr[2k, 4k]] == n, Return[k]]]; 0]; Table[a[n], {n, 0, 16387}] (* _Jean-François Alcover_, Feb 23 2016 *)

%o (Scheme)

%o (define (A269162 n) (let loop ((p 0)) (cond ((= n (A269160 p)) p) ((> p n) 0) (else (loop (+ 1 p)))))) ;; Very slow implementation.

%o (define (A269162 n) (if (zero? n) n (let ((nwid-2 (- (A000523 n) 2))) (let loop ((p (if (< n 4) 0 (A000079 nwid-2)))) (let ((k (A269160 p))) (cond ((= n k) p) ((> (A000523 p) nwid-2) 0) (else (loop (+ 1 p))))))))) ;; Somewhat optimized.

%Y Cf. A110240, A269160, A269163, A269164 (indices of zeros), A269165, A269166.

%K nonn

%O 0,14

%A _Antti Karttunen_, Feb 20 2016