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

Author

Antti Karttunen, Feb 21 2016

Keywords

• nonn

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

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.

Programs

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)))))

Formula

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