A270814 - OEIS

%I #51 Dec 11 2022 01:24:29

%S 0,1,46,3,31,49,281,7,330,36,248,55,106,288,679,15,197,339,500,46,127,

%T 259,610,67,633,119,101413,302,413,694,101073,31,808,214,505,357,498,

%U 519,2305,66,101290,148,1295,281,452,633,100932,91,757,658,1079,145,346,101440,102261,330,1596,442,2128

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

%C Inspired by A266569.

%C In other words, a(n) = n/2 + a(n/2) if n even, a(n) = 3n+1+a(3n+1) if n odd.

%C From _Seiichi Manyama_, Apr 25 2016: (Start)

%C This sequence was inspired by the Collatz problem (A006577).

%C The Collatz rule is as follows: If n is even, divide it by 2, otherwise multiply it by 3 and add 1 (A006370).

%C 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]

%H Seiichi Manyama, <a href="/A270814/b270814.txt">Table of n, a(n) for n = 1..20000</a>

%H Seiichi Manyama, <a href="/A270814/a270814.txt">Table of n, a(n) for n = 1..650289</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%p A270814 := proc(n)

%p         local a, traj ;

%p         a := 0 ;

%p         traj := n ;

%p         while traj > 1 do

%p                 if type(traj, 'even') then

%p                         traj := traj/2 ;

%p                 else

%p                         traj := 3*traj+1 ;

%p                 end if;

%p                 a := a+traj ;

%p         end do:

%p         return a;

%p end proc:

%p [seq(A270814(n),n=1..60)];

%o (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

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

%Y Cf. A266569, A271473.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Apr 08 2016

%E Typo in definition corrected by _Gionata Neri_, Apr 08 2016