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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.
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%I #7 May 09 2017 00:06:52

%S 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,

%T 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,

%U 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

%N 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.

%H Antti Karttunen, <a href="/A286380/b286380.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

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

%F Other identities. For all n >= 1:

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

%o (Scheme) (define (A286380 n) (if (= 1 n) 0 (+ 1 (A286380 (A139391 n)))))

%Y Cf. A075680 (the odd bisection).

%Y Cf. A078719, A139391.

%K nonn

%O 1,3

%A _Antti Karttunen_, May 08 2017