A055509 Number of odd primes in sequence obtained in 3x+1 (or Collatz) problem starting at n.

0, 0, 2, 0, 1, 2, 5, 0, 5, 1, 4, 2, 2, 5, 3, 0, 3, 5, 6, 1, 0, 4, 3, 2, 6, 2, 24, 5, 5, 3, 23, 0, 6, 3, 2, 5, 6, 6, 10, 1, 24, 0, 7, 4, 3, 3, 22, 2, 6, 6, 5, 2, 2, 24, 23, 5, 7, 5, 10, 3, 4, 23, 19, 0, 6, 6, 8, 3, 2, 2, 21, 5, 24, 6, 1, 6, 5, 10, 10, 1, 4, 24, 23, 0, 0, 7, 8, 4, 9, 3, 19, 3, 2, 22, 19

Offset

1,3

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Collatz Problem

Wikipedia, Collatz conjecture

Index entries for sequences related to 3x+1 (or Collatz) problem

Formula

a(n) = A078350(n) - 1 for n > 1.

a(A196871(n)) = 0. - Reinhard Zumkeller, Oct 08 2011

From Robert Israel, Dec 05 2017: (Start)

If n is odd, a(n) = a(3*n+1) + A010051(n).

If n is even, a(n) = a(n/2). (End)

Maple

g:= proc(n) option remember;
   local x;
   x:= 3*n+1;
   x:= x/2^padic:-ordp(x, 2);
   if isprime(n) then procname(x)+1 else procname(x) fi
end proc:
g(1):= 0:
seq(g(n/2^padic:-ordp(n, 2)), n=1..100); # Robert Israel, Dec 05 2017

Mathematica

Join[{0}, Table[Count[NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &], _?PrimeQ] - 1, {n, 2, 94}]] (* Jayanta Basu, Jun 15 2013 *)

Prog

(Haskell) a055509 n = sum $ map a010051 $ takeWhile (> 2) $ iterate a006370 n -- Reinhard Zumkeller, Oct 08 2011
(PARI) A078350(n, c=0)={while(1<n>>=valuation(n, 2), isprime(n)&&c++; n=n*3+1); c} \\ M. F. Hasler, Dec 05 2017

Crossrefs

Cf. A055510.

Cf. A006370, A010051.

Sequence in context: A341439 A127767 A292577 * A334226 A006667 A112570

Adjacent sequences: A055506 A055507 A055508 * A055510 A055511 A055512

Keyword

nonn

Author

G. L. Honaker, Jr., Jun 30 2000

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Aug 09 2001

Status

approved