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

Author

N. J. A. Sloane, Apr 10 2016

Keywords

• nonn

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

Crossrefs

Cf. A266569, A271478, A000120, A023416.

Programs

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 *)

PARI

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

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