A137843 Define S(1) = {1}, S(n+1) = S(n) U S(n) if a(n) is even, S(n+1) = S(n) U (n+1) U S(n) if a(n) is odd. Sequence {a(n), n >= 1} is limit as n approaches infinity of S(n). (U represents concatenation.).

1, 2, 1, 1, 2, 1, 4, 1, 2, 1, 1, 2, 1, 5, 1, 2, 1, 1, 2, 1, 4, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 4, 1, 2, 1, 1, 2, 1, 5, 1, 2, 1, 1, 2, 1, 4, 1, 2, 1, 1, 2, 1, 7, 1, 2, 1, 1, 2, 1, 4, 1, 2, 1, 1, 2, 1, 5, 1, 2, 1, 1, 2, 1, 4, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 4, 1, 2, 1, 1, 2, 1, 5, 1, 2, 1, 1, 2, 1, 4, 1, 2, 1, 1, 2, 1

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..27995, up to the stage S(15)

Example

S(1) = {1}.
S(2) = {1,2,1}, because a(1) = 1, which is odd.
S(3) = {1,2,1,1,2,1}, because a(2) = 2, which is even.
S(4) = {1,2,1,1,2,1,4,1,2,1,1,2,1}, as a(3) is odd.
S(5) = {1,2,1,1,2,1,4,1,2,1,1,2,1,5,1,2,1,1,2,1,4,1,2,1,1,2,1}, as a(4) is odd.
Etc.

Prog

(Scheme, with memoization-macro definec)
(definec (A137843 n) (if (= 1 n) n (let ((k (let loop ((j 1)) (if (>= (A291753 j) n) j (loop (+ 1 j)))))) (cond ((= (+ 1 (A291753 (- k 1))) n) (if (odd? (A137843 (- k 1))) k 1)) (else (A137843 (- n (+ (A291753 (- k 1)) (A000035 (A137843 (- k 1)))))))))))
(definec (A291753 n) (if (= 1 n) 1 (+ (* 2 (A291753 (- n 1))) (A000035 (A137843 (- n 1))))))
(define (A000035 n) (modulo n 2))
;; Antti Karttunen, Aug 31 2017

Crossrefs

Cf. A096055, A137844 (variants of the same theme).

Cf. A291753 (the length of stage n).

Sequence in context: A266685 A272620 A304080 * A130194 A113926 A276376

Adjacent sequences: A137840 A137841 A137842 * A137844 A137845 A137846

Keyword

easy,nonn

Author

Leroy Quet, Feb 13 2008

Extensions

More terms from Antti Karttunen, Aug 31 2017

Status

approved