A140259 a(0)=3; a(n)=A002264(n+11) if a(n-1)=1, a(n) = a(n-1)-1 if (n-1) mod 3 <> 0, otherwise a(n-1).

3, 3, 2, 1, 5, 4, 3, 3, 2, 1, 7, 6, 5, 5, 4, 3, 3, 2, 1, 10, 9, 8, 8, 7, 6, 6, 5, 4, 4, 3, 2, 2, 1, 14, 14, 13, 12, 12, 11, 10, 10, 9, 8, 8, 7, 6, 6, 5, 4, 4, 3, 2, 2, 1, 21, 21, 20, 19, 19, 18, 17, 17, 16, 15, 15, 14, 13, 13, 12, 11, 11, 10, 9, 9, 8, 7, 7, 6, 5, 5, 4, 3, 3, 2, 1, 32, 31

Offset: 0

Author

Antti Karttunen, May 16 2008, based on the 2008 postings by Nicolau Leal Werneck (nwerneck(AT)gmail.com)

Keywords

• nonn

Comments

Position of the knot after each iteration in Werneck's Black Pearl Necklace problem.

Links

• Nicolau Werneck, Adaptoide, a library for adaptive finite automata. Source code in C++ available.
• Nicolau Werneck, The Black Pearl Necklace, description of the problem.
• Nicolau Werneck, et al. Discussion on the NKS Forum

Crossrefs

Cf. A134342, A140260, A140261.

Programs

Scheme

(define (A140259 n) (cond ((zero? n) 3) ((= 1 (A140259 (- n 1))) (A002264 (+ n 11))) ((not (zero? (modulo (- n 1) 3))) (- (A140259 (- n 1)) 1)) (else (A140259 (- n 1)))))