A368878 - OEIS

%I #20 Sep 30 2024 15:47:45

%S 2,1,1,2,3,1,2,1,2,1,1,2,2,1,1,1,1,1,1,1,1,1,1,1,8,1,1,2,8,1,2,1,1,1,

%T 1,1,2,1,8,1,2,1,1,1,8,1,1,1,1,1,1,7,7,1,2,1,2,2,2,8,8,1,1,1,1,1,1,1,

%U 6,1,1,1,1,1,1,2,2,1,1,7,7,1,1,1,1,1,1,1,6,1

%N a(n) is the least k such that A368877^k(n) < n or -1 if no such k exists.

%C This is the falling time function ft in the paper of Eliahou et al.

%C The offset is 3 because A368877(1) = A368877(2) = 2, so for n<3 is not defined.

%H Paolo Xausa, <a href="/A368878/b368878.txt">Table of n, a(n) for n = 3..10000</a>

%H Shalom Eliahou, Jean Fromentin, and Rénald Simonetto, <a href="https://hal.science/hal-03294829">Is the Syracuse falling time bounded by 12?</a>, hal-03294829, 2021.

%t A368877[n_] := Nest[If[OddQ[#], (3*#+1)/2, #/2] &, n, BitLength[n]];

%t A368878[n_] := Length[NestWhileList[A368877, n, #>=n&]]-1;

%t Array[A368878, 120, 3] (* _Paolo Xausa_, Jan 08 2024 *)

%o (PARI) T(n) = if (n%2, (3*n+1)/2, n/2); \\ A014682

%o jp(n) = my(N=1+logint(n, 2)); for (i=1, N, n = T(n)); n; \\ A368877

%o a(n) = my(k=1, m=n); while ((m=jp(m)) >= n, k++); k;

%Y Cf. A014682, A070939, A368877.

%K nonn

%O 3,1

%A _Michel Marcus_, Jan 08 2024