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

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

Author

N. J. A. Sloane, Apr 08 2016

Keywords

• nonn

Comments

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]

Links

• 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

Crossrefs

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

Cf. A266569, A271473.

Programs

Maple

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)];

PARI

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

Extensions

Typo in definition corrected by Gionata Neri, Apr 08 2016