A261870 a(n) = minimal number of steps to get from n to 1, where a step is x -> 3x-1 if x is odd, or x -> either x/2 or 3x-1 if x is even.

0, 1, 4, 2, 15, 5, 13, 3, 16, 11, 6, 6, 19, 14, 9, 4, 35, 17, 17, 12, 25, 7, 20, 7, 33, 15, 15, 15, 10, 10, 23, 5, 36, 36, 18, 18, 31, 18, 13, 13, 26, 26, 8, 8, 26, 21, 21, 8, 34, 34, 21, 16, 16, 16, 29, 16, 29, 11, 11, 11, 24, 24, 24, 6, 37, 37, 24, 19, 19, 19, 19, 19, 32, 32, 19, 19, 14, 14, 14, 14, 27, 27, 27, 27, 27, 9, 40, 9, 27, 27, 22, 22, 22, 22, 22, 9, 35, 35, 35, 22

Offset: 1

Author

Max Alekseyev, Sep 03 2015

Keywords

• nonn

Comments

The 3x-1 variation of Collatz conjecture would imply that this sequence is well defined. In turn, if this sequence is well-defined, then A109732 represents a permutation of the odd positive integers.

Links

• Kevin Ryde, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Max Alekseyev)
• Kevin Ryde, C Code

Crossrefs

Cf. A127885, A006577, A109732.

Programs

C

/* See links. */

PARI

{ A261870(n) = my(S, k); S=[n]; k=0; while( S[1]!=1, k++; S=vecsort( concat(apply(x->3*x-1, S), apply(x->x\2, select(x->x%2==0, S) )), , 8);  ); k } /* Max Alekseyev, Sep 03 2015 */