%I #14 Oct 20 2022 16:26:14

%S 0,2,1,6,7,5,3,7,4,8,2,6,9,48,7,46,10,5,8,14,47,11,6,45,9,10,4,49,12,

%T 13,8,47,10,11,5,44,50,5,9,15,9,48,3,12,12,40,7,46,51,10,10,38,16,43,

%U 49,30,4,13,8,14,41,19,47,20,52,11,11,16,39,17,6

%N The minimal number of iterations to reach 1 of the modified reduced Collatz function, defined for odd numbers 1 + 2*n in A324036 (assuming the Collatz conjecture).

%C The Collatz conjecture is that a(n) is finite. If 1 should never be reached then a(n) = -1.

%C Compare this sequence with the analogous one A075680(n+1) for the reduced Collatz map of A075677.

%C a(n) gives also the minimal number of iterations of the Vaillant-Delarue map f, defined in A324245, acting on n to reach 0 (assuming the Collatz conjecture).

%C For the link to the Vaillant-Delarue paper (where fs is called f_s) see A324036.

%F fs^[a(n)](1 + 2*n) = 1 but fs^[a(n)-1](1 + 2*n) is not 1 (for all n with finite a(n)), where fs is the modified reduced Collatz map defined for 1 + 2*n in A324036(n), for n >= 1, and a(0) = 0.

%e a(4) = 7 because 1 + 2*4 = 9 and the 7 fs iterations acting on 9 are 7, 11, 17, 13, 3, 5, 1.

%e Compare this to the reduced Collatz map given in A075677 which needs only 6 = A075680(5) iterations 7, 11, 17, 13, 5, 1. The additional step in the fs case follows 13 == 5 mod(8).

%Y Cf. A075677, A075680(n+1), A324036, A324245.

%K nonn

%O 0,2

%A _Nicolas Vaillant_, Philippe Delarue, _Wolfdieter Lang_, May 09 2019