A271478 -id:A271478 - cp's OEIS frontend

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

N. J. A. Sloane, Apr 10 2016

nonn

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, ...

N. J. A. Sloane, Table of n, a(n) for n = 1..10000
Christian Krause, LODA program for A271479

Cf. A266569, A271478, A000120, A023416.

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;

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

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

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

A266569 a(1) = 1; thereafter a(2k) = 4k + a(k); a(2k+1) = k + a(4k+4).

Original entry on oeis.org

1, 5, 30, 13, 68, 42, 64, 29, 132, 88, 119, 66, 154, 92, 132, 61, 248, 168, 217, 128, 261, 163, 221, 114, 322, 206, 273, 148, 326, 192, 268, 125, 468, 316, 401, 240, 463, 293, 387, 208, 533, 345, 448, 251, 519, 313, 425, 210, 646, 422, 543, 310, 623, 381, 511

Offset: 1

Daniel Suteu, Jan 01 2016

			For n=2, a(2) = 4 + a(1) = 5.
For n=3:
a(3) = 1 + a(8);
a(8) = 2*8 + a(8/2) = 16 + a(4);
a(4) = 2*4 + a(4/2) = 8 + a(2) = 13;
a(8) = 18+13 = 29;
a(3) = 1 + 29 = 30.

Daniel Suteu, Table of n, a(n) for n = 1..10000
Daniel Suteu, Table of n, a(n) for n = 1..100000

Records (high water marks): A270811, A270812.

Cf. A270814, A271473, A271478, A271479.

A266569 := proc(n)
    option remember;
    local k;
    if n = 1 then
        1;
    elif type(n,'even') then
        2*n+procname(n/2) ;
    else
        k := (n-1)/2 ;
        k+procname(4*k+4) ;
    end if;
end proc:
seq(A266569(n),n=1..100) ; # R. J. Mathar, May 06 2016

a[1] = 1; a[n_] := a[n] = If[EvenQ@ n, 2 n + a[n/2], (n - 1)/2 + a[2 (n + 1)]]; Array[a, 55] (* Michael De Vlieger, Jan 02 2016 *)

func a((1)) { 1 }
func a(n {.is_even}) is cached { 2*n + a(n/2) }
func a(n {.is_odd }) is cached { (n-1)/2 + a(2*(n + 1)) }
1000.times { |n| say a(n) }

cp's OEIS Frontend

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

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