A286380 a(n) = the minimum number of iterations of the reduced Collatz function R required to yield 1. The function R (A139391) is defined as R(k) = (3k+1)/2^r, with r as large as possible.

0, 1, 2, 1, 1, 3, 5, 1, 6, 2, 4, 3, 2, 6, 5, 1, 3, 7, 6, 2, 1, 5, 4, 3, 7, 3, 41, 6, 5, 6, 39, 1, 8, 4, 3, 7, 6, 7, 11, 2, 40, 2, 9, 5, 4, 5, 38, 3, 7, 8, 7, 3, 2, 42, 41, 6, 10, 6, 10, 6, 5, 40, 39, 1, 8, 9, 8, 4, 3, 4, 37, 7, 42, 7, 3, 7, 6, 12, 11, 2, 6, 41, 40, 2, 1, 10, 9, 5, 9, 5, 33, 5, 4, 39, 38, 3, 43, 8, 7, 8, 7, 8, 31, 3, 12, 3, 36, 42, 41, 42, 24

Offset: 1

Author

Antti Karttunen, May 08 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A075680 (the odd bisection).

Cf. A078719, A139391.

Programs

Scheme

(define (A286380 n) (if (= 1 n) 0 (+ 1 (A286380 (A139391 n)))))

Formula

a(1) = 0; for n > 1, a(n) = 1 + a(A139391(n)).

Other identities. For all n >= 1:

a(n) + A000035(n) = A078719(n).