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A269165 If A269162(n) = 0, then a(n) = n, otherwise a(n) = a(A269162(n)).

%I A269165 #14 Feb 16 2025 08:33:30
%S A269165 0,1,2,3,4,5,6,1,8,9,10,11,12,3,2,15,16,17,18,19,20,21,22,23,24,1,6,5,
%T A269165 4,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,15,2,3,
%U A269165 12,11,10,55,8,57,58,59,60,61,62,9,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81
%N A269165 If A269162(n) = 0, then a(n) = n, otherwise a(n) = a(A269162(n)).
%C A269165 a(n) is the earliest finite ancestor pattern n in Rule-30 or n itself if n has no finite predecessors.
%C A269165 Starting from k = a(n) with any n and iterating map k -> A269160(k) exactly A269166(n) times yields n back.
%C A269165 Apart from zero no terms of A269163 occur so all terms after zero are in A269164. Each term of A269164 occurs an infinitely many times.
%H A269165 Antti Karttunen, <a href="/A269165/b269165.txt">Table of n, a(n) for n = 0..32767</a>
%H A269165 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule30.html">Rule 30</a>
%H A269165 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A269165 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A269165 If A269162(n) = 0, then a(n) = n, otherwise a(n) = a(A269162(n)).
%o A269165 (Scheme)
%o A269165 ;; This implementation is based on given recurrence and utilitizes the memoization-macro definec:
%o A269165 (definec (A269165 n) (let ((p (A269162 n))) (if (zero? p) n (A269165 p))))
%o A269165 ;; This one computes the same with tail-recursive iteration:
%o A269165 (define (A269165 n) (let loop ((n n) (p (A269162 n))) (if (zero? p) n (loop p (A269162 p)))))
%Y A269165 Cf. A269160, A269163, A269164, A269166 (for a distance in A269162-steps to the ancestor pattern).
%Y A269165 Cf. A110240 (indices of ones in this sequence).
%Y A269165 Cf. also A268669.
%K A269165 nonn
%O A269165 0,3
%A A269165 _Antti Karttunen_, Feb 21 2016