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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.
2
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, 26, 80, 242, 2, 44, 5, 5, 17, 17, 17, 152, 2, 161, 2, 56, 20, 20, 20, 182, 8, 7, 22, 22, 8, 8, 71, 71, 26, 74, 26, 76, 80, 80, 242, 728, 2, 14, 44, 44, 5, 5, 5, 137, 17, 47, 17, 16
OFFSET
1,1
COMMENTS
This is the jump function jp in the paper of Eliahou et al.
LINKS
Shalom Eliahou, Jean Fromentin, and Rénald Simonetto, Is the Syracuse falling time bounded by 12?, hal-03294829, 2021.
MATHEMATICA
A368877[n_] := Nest[If[OddQ[#], (3*#+1)/2, #/2]&, n, BitLength[n]];
Array[A368877, 100] (* Paolo Xausa, Jan 08 2024 *)
PROG
(PARI) T(n) = if (n%2, (3*n+1)/2, n/2); \\ A014682
a(n) = my(N=1+logint(n, 2)); for (i=1, N, n = T(n)); n;
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Jan 08 2024
STATUS
approved