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A368877 a(n) = f^k(n) where f(n) = A014682(n), the Collatz map, and k = A070939(n), the length of n in base 2.

%I A368877 #19 Sep 30 2024 15:47:34
%S A368877 2,2,8,2,2,8,26,2,17,2,20,8,8,26,80,2,5,17,17,2,2,20,20,8,22,8,71,26,
%T A368877 26,80,242,2,44,5,5,17,17,17,152,2,161,2,56,20,20,20,182,8,7,22,22,8,
%U A368877 8,71,71,26,74,26,76,80,80,242,728,2,14,44,44,5,5,5,137,17,47,17,16
%N A368877 a(n) = f^k(n) where f(n) = A014682(n), the Collatz map, and k = A070939(n), the length of n in base 2.
%C A368877 This is the jump function jp in the paper of Eliahou et al.
%H A368877 Paolo Xausa, <a href="/A368877/b368877.txt">Table of n, a(n) for n = 1..10000</a>
%H A368877 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 A368877[n_] := Nest[If[OddQ[#], (3*#+1)/2, #/2]&, n, BitLength[n]];
%t A368877 Array[A368877, 100] (* _Paolo Xausa_, Jan 08 2024 *)
%o A368877 (PARI) T(n) = if (n%2, (3*n+1)/2, n/2); \\ A014682
%o A368877 a(n) = my(N=1+logint(n, 2)); for (i=1, N, n = T(n)); n;
%Y A368877 Cf. A014682, A070939, A368878.
%K A368877 nonn
%O A368877 1,1
%A A368877 _Michel Marcus_, Jan 08 2024