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

Author

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

Keywords

• nonn

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

Crossrefs

Cf. A055510.

Cf. A006370, A010051.

Programs

Haskell

a055509 n = sum $ map a010051 $ takeWhile (> 2) $ iterate a006370 n -- Reinhard Zumkeller, Oct 08 2011

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 *)

PARI

A078350(n,c=0)={while(1>=valuation(n,2), isprime(n)&&c++; n=n*3+1);c} \\ M. F. Hasler, Dec 05 2017

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)

Extensions

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