A056957 In repeated iterations of function m->m/2 if m even, m->3m-1 if m odd, a(n) is minimum value achieved if starting from n.

1, 1, 1, 1, 5, 1, 5, 1, 5, 5, 1, 1, 5, 5, 1, 1, 17, 5, 5, 5, 17, 1, 17, 1, 17, 5, 5, 5, 1, 1, 17, 1, 17, 17, 5, 5, 17, 5, 1, 5, 17, 17, 1, 1, 17, 17, 5, 1, 17, 17, 5, 5, 1, 5, 17, 5, 1, 1, 1, 1, 17, 17, 5, 1, 1, 17, 17, 17, 1, 5, 1, 5, 17, 17, 5, 5, 1, 1, 1, 5, 5, 17, 17, 17, 1, 1, 1, 1, 5, 17

Offset

1,5

Comments

At least for n<10000, the only possible cycles reached include 1,2,1,..., 5,14,7,20,10,5,... and 17,50,25,74,37,110,55,164,82,41,122,61,182,91,272,136,68,34,17,... For n<5 only the first occurs, while for n<17 only the first two occur.

Links

Table of n, a(n) for n=1..90.

Formula

a(2n) = a(n)

Example

a(9)=5 since iteration starts: 9, 26, 13, 38, 19, 56, 28, 14, 7, 20, 10, 5, 14, 7, 20, 10, 5, ... and 5 is the smallest value

Crossrefs

Cf. A001281. If n is in A039500 then a(n)=1, if n is in A039501 then a(n)=5, if n is in A039502 then a(n)=17. If n is negative then this becomes the 3x+1 problem and the minimum values become those which are most negative (i.e. maximum absolute values) as in A056959.

Sequence in context: A339353 A050349 A083528 * A224834 A095118 A251417

Adjacent sequences: A056954 A056955 A056956 * A056958 A056959 A056960

Keyword

nonn

Author

Henry Bottomley, Jul 18 2000

Extensions

Edited by Bryce Herdt (mathidentity(AT)yahoo.com), Apr 18 2010

Status

approved