A095381 Initial values for 3x+1 trajectories in which the largest term arising in the iteration is a power of 2.

1, 2, 3, 4, 5, 6, 8, 10, 12, 16, 21, 32, 42, 64, 85, 128, 151, 170, 201, 227, 256, 302, 341, 402, 454, 512, 604, 682, 804, 908, 1024, 1365, 2048, 2730, 4096, 5461, 8192, 10922, 14563, 16384, 19417, 21845, 29126, 32768, 38834, 43690, 58252, 65536, 87381

Offset: 1

Author

Labos Elemer, Jun 14 2004

Keywords

• nonn

Comments

Clearly the sequence is infinite and a(n) < 2^n. - Charles R Greathouse IV, May 25 2016

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A025586, A087256, A209229, A225124.

Programs

C

// Valid below A006884(47) = 12327829503 on 64-bit machines.
static long is (unsigned long n) {
  unsigned long r = n;
  n >>= __builtin_ctzl(n); // gcc builtin for A007814
  while (n > 1) {
    n = 3*n + 1;
    if (n > r) r = n;
    n >>= __builtin_ctzl(n);
  }
  return !(r & (r-1));
} // Charles R Greathouse IV, May 25 2016

Haskell

a095381 n = a095381_list !! (n-1)
a095381_list = map (+ 1) $ elemIndices 1 $ map a209229 a025586_list
-- Reinhard Zumkeller, Apr 30 2013

Mathematica

Coll[n_]:=NestWhileList[If[EvenQ[#],#/2,3*#+1] &,n,#>1&];t={};Do[x = Max[Coll[n]];If[IntegerQ[Log[2,x]],AppendTo[t,n]],{n,90000}];t (* Jayanta Basu, Apr 28 2013 *)

PARI

is(n)=my(r=n); while(n>2, if(n%2, n=3*n+1; if(n>r, r=n)); n>>=1); r>>valuation(r,2)==1 \\ Charles R Greathouse IV, May 25 2016

Formula

A025586(a(n)) = 2^j for some j.