A137844 Define S(1) = {1}, S(n+1) = S(n) U S(n) if a(n) is even, S(n+1) = S(n) U n 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, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..31739, up to the stage S(15)

Example

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

Mathematica

Fold[Flatten@ Join[#1, If[OddQ[#1[[#2]]], {#2}, {}], #1] &, {1}, Range@ 6] (* Michael De Vlieger, Oct 18 2017 *)

Prog

(Scheme, with memoization-macro definec)
(definec (A137844 n) (if (= 1 n) n (let ((k (let loop ((j 1)) (if (>= (A291754 j) n) j (loop (+ 1 j)))))) (cond ((= (+ 1 (A291754 (- k 1))) n) (if (odd? (A137844 (- k 1))) (- k 1) 1)) (else (A137844 (- n (+ (A291754 (- k 1)) (A000035 (A137844 (- k 1)))))))))))
(definec (A291754 n) (if (= 1 n) 1 (+ (* 2 (A291754 (- n 1))) (A000035 (A137844 (- n 1))))))
(define (A000035 n) (modulo n 2))
;; Antti Karttunen, Aug 31 2017

Crossrefs

Cf. A137843, A291754 (the length of stage n).

Sequence in context: A111946 A175788 A237513 * A263845 A079229 A344972

Adjacent sequences: A137841 A137842 A137843 * A137845 A137846 A137847

Keyword

easy,nonn

Author

Leroy Quet, Feb 13 2008

Extensions

Data section filled up to the length of stage S(7) by Antti Karttunen, Aug 31 2017

Status

approved