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

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, 4, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 15, 2, 3, 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

Offset

0,3

Comments

a(n) is the earliest finite ancestor pattern n in Rule-30 or n itself if n has no finite predecessors.

Starting from k = a(n) with any n and iterating map k -> A269160(k) exactly A269166(n) times yields n back.

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.

Links

Antti Karttunen, Table of n, a(n) for n = 0..32767

Eric Weisstein's World of Mathematics, Rule 30

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

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

Prog

(Scheme)
;; This implementation is based on given recurrence and utilitizes the memoization-macro definec:
(definec (A269165 n) (let ((p (A269162 n))) (if (zero? p) n (A269165 p))))
;; This one computes the same with tail-recursive iteration:
(define (A269165 n) (let loop ((n n) (p (A269162 n))) (if (zero? p) n (loop p (A269162 p)))))

Crossrefs

Cf. A269160, A269163, A269164, A269166 (for a distance in A269162-steps to the ancestor pattern).

Cf. A110240 (indices of ones in this sequence).

Cf. also A268669.

Sequence in context: A355582 A160377 A373028 * A319655 A328018 A242603

Adjacent sequences: A269162 A269163 A269164 * A269166 A269167 A269168

Keyword

nonn,changed

Author

Antti Karttunen, Feb 21 2016

Status

approved