A271479 Number of steps for the trajectory of n under the map k -> A271478(k) to reach 1.

0, 1, 4, 2, 7, 5, 5, 3, 10, 8, 8, 6, 8, 6, 6, 4, 13, 11, 11, 9, 11, 9, 9, 7, 11, 9, 9, 7, 9, 7, 7, 5, 16, 14, 14, 12, 14, 12, 12, 10, 14, 12, 12, 10, 12, 10, 10, 8, 14, 12, 12, 10, 12, 10, 10, 8, 12, 10, 10, 8, 10, 8, 8, 6, 19, 17, 17, 15, 17, 15, 15, 13, 17, 15, 15, 13, 15, 13

Offset

1,3

Comments

Arises in studying A266569.

Records are 0, 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, ... and occur at positions 1, 2, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, ...

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Christian Krause, LODA program for A271479

Formula

a(1) = 0; a(2*n) = a(n)+1; a(2*n+1) = a(n+1)+3. - Christian Krause, Mar 19 2021

a(n) = A000120(n-1) + 3*A023416(n-1), for n>=2. - Kevin Ryde, Mar 21 2021

Maple

f:=n->if n mod 2 = 0 then n/2 else 2*n+2; fi; # A271478
a:=[]; B:=1000;
for n from 1 to 100 do
   ct:=0; s:=n;
   for k from 1 to B while s>1 do
   s:=f(s); ct:=ct+1; od:
if ct=B then lprint("error, need to increase limit B"); break; fi;
a:=[op(a), ct]; od:
a;

Mathematica

Table[Length[NestWhileList[If[EvenQ[#], #/2, 2#+2]&, n, #!=1&]]-1, {n, 80}] (* Harvey P. Dale, May 02 2017 *)

Prog

(PARI) a(n) = if(n--, 3*(logint(n, 2)+1) - 2*hammingweight(n), 0); \\ Kevin Ryde, Mar 21 2021

Crossrefs

Cf. A266569, A271478, A000120, A023416.

Sequence in context: A115302 A109857 A194075 * A259927 A002560 A124908

Adjacent sequences: A271476 A271477 A271478 * A271480 A271481 A271482

Keyword

nonn

Author

N. J. A. Sloane, Apr 10 2016

Status

approved