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

1,2

Links

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

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A006577.

Sequence in context: A299556 A282978 A125719 * A265763 A064024 A284085

Adjacent sequences: A070972 A070973 A070974 * A070976 A070977 A070978

Keyword

easy,nonn

Author

Benoit Cloitre, May 17 2002

Status

approved