A271473 -id:A271473 - cp's OEIS frontend

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

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) }

A270814 a(1)=0; thereafter a(2k)=k+a(k), a(2k+1)=6k+4+a(6k+4).

Original entry on oeis.org

0, 1, 46, 3, 31, 49, 281, 7, 330, 36, 248, 55, 106, 288, 679, 15, 197, 339, 500, 46, 127, 259, 610, 67, 633, 119, 101413, 302, 413, 694, 101073, 31, 808, 214, 505, 357, 498, 519, 2305, 66, 101290, 148, 1295, 281, 452, 633, 100932, 91, 757, 658, 1079, 145, 346, 101440, 102261, 330, 1596, 442, 2128

Offset: 1

N. J. A. Sloane, Apr 08 2016

nonn

Inspired by A266569.
In other words, a(n) = n/2 + a(n/2) if n even, a(n) = 3n+1+a(3n+1) if n odd.
From Seiichi Manyama, Apr 25 2016: (Start)
This sequence was inspired by the Collatz problem (A006577).
The Collatz rule is as follows: If n is even, divide it by 2, otherwise multiply it by 3 and add 1 (A006370).
For example, starting with n = 3, one gets the sequence 3, 10, 5, 16, 8, 4, 2, 1. So a(3) = 10 + 5 + 16 + 8 + 4 + 2 + 1 = 46. (End) [Comment edited by N. J. A. Sloane, Apr 25 2016]

Seiichi Manyama, Table of n, a(n) for n = 1..20000
Seiichi Manyama, Table of n, a(n) for n = 1..650289
Index entries for sequences related to 3x+1 (or Collatz) problem

Cf. A006370 (Collatz step), A006577 (trajectory length), A033493 (sum including n).

Cf. A266569, A271473.

A270814 := proc(n)
        local a, traj ;
        a := 0 ;
        traj := n ;
        while traj > 1 do
                if type(traj, 'even') then
                        traj := traj/2 ;
                else
                        traj := 3*traj+1 ;
                end if;
                a := a+traj ;
        end do:
        return a;
end proc:
[seq(A270814(n),n=1..60)];

a(n) = my(ret=n-1); while((n>>=valuation(n,2)) > 1, ret+=5*n+2; n=3*n+1); ret; \\ Kevin Ryde, Dec 10 2022

Typo in definition corrected by Gionata Neri, Apr 08 2016

cp's OEIS Frontend

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

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