A226614 Positive integers k for which 1 is in a cycle of integers under iteration by the Collatz-like 3x+k function.

1, 5, 11, 13, 17, 29, 41, 43, 55, 59, 61, 77, 79, 91, 95, 97, 107, 113, 119, 125, 127, 137, 145, 155, 185, 193, 203, 209, 215, 239, 247, 253, 257, 275, 281, 289, 317, 329, 335, 353, 355, 407, 437, 445, 473, 493, 499, 509, 553, 559, 593, 629, 637, 643, 673, 697

Offset

1,2

Comments

The 3x+k function T_k is defined by T_k(x) = x/2 if x is even, (3x+k)/2 if x is odd. GCD(k,6)=1.

When k=2^m-3, T_k has a cycle containing 1. Hence the sequence is infinite.

a(n) is in the sequence if and only if A226607(A226612(floor(a(n)/3)+1)) = 1.

Trivially, members of the sequence are not divisible by 2 or 3. Of the first 10^4 members, only 1,066 are squareful, which is about one third of the expected density. - Ralf Stephan, Aug 05 2013

Links

Geoffrey H. Morley, Table of n, a(n) for n = 1..10000

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

Prog

(PARI) \\ 5.5 hours (2.33 Ghz Intel Core 2)
{k=1; n=1;
until(n>10000, x=1; y=1; len=0;
  until(x==y, if(x%2==0, x=x/2, x=(3*x+k)/2);
    if(y%2==0, y=y/2, y=(3*y+k)/2);
    if(y%2==0, y=y/2, y=(3*y+k)/2); len++);
  if(x==1, write("b226614.txt", n, " ", k);
    write("b226615.txt", n, " ", len); n++);
  k+=(k+3)%6)}

Crossrefs

Cf. A226615-A226618.

Sequence in context: A019354 A230288 A124662 * A328058 A191042 A049511

Adjacent sequences: A226611 A226612 A226613 * A226615 A226616 A226617

Keyword

nonn

Author

Geoffrey H. Morley, Aug 02 2013

Status

approved