A070975 Number of steps to reach 1 in `3x+1' (or Collatz) problem starting with prime(n).

1, 7, 5, 16, 14, 9, 12, 20, 15, 18, 106, 21, 109, 29, 104, 11, 32, 19, 27, 102, 115, 35, 110, 30, 118, 25, 87, 100, 113, 12, 46, 28, 90, 41, 23, 15, 36, 23, 67, 31, 31, 18, 44, 119, 26, 119, 39, 70, 13, 34, 83, 52, 21, 65, 122, 78, 29, 42, 16, 42, 60, 117, 37, 86, 130, 37, 24

Offset: 1

Author

Benoit Cloitre, May 17 2002

Keywords

• easy
• nonn

Links

• T. D. Noe, Table of n, a(n) for n=1..10000

Crossrefs

Cf. A006577.

Programs

Mathematica

ns[n_]:=Length[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#!=1&]]-1; ns/@ Prime[Range[70]] (* Harvey P. Dale, Jul 29 2014 *)

PARI

for(n=2,100,s=prime(n); t=0; while(s!=1,t++; if(s%2==0,s=s/2,s=3*s+1); if(s==1,print1(t,","); ); ))

Python

from sympy import prime
def a006577(n):
    if n==1: return 0
    x=0
    while True:
        if n%2==0: n//=2
        else: n = 3*n + 1
        x+=1
        if n<2: break
    return x
def a(n): return a006577(prime(n))
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jun 05 2017

Formula

a(n) = A006577(prime(n)). - Michel Marcus, Sep 07 2014