|
| |
|
|
A138752
|
|
Number of iterations before prime(n) reaches 7 or 2 under x -> A007918(A138750(x)).
|
|
3
| |
|
|
0, 1, 2, 0, 1, 4, 2, 7, 5, 3, 20, 16, 6, 6, 4, 4, 21, 23, 19, 17, 17, 15, 7, 5, 7, 5, 28, 22, 26, 22, 22, 20, 18, 18, 16, 20, 16, 14, 6, 6, 8, 59, 8, 8, 6, 29, 27, 25, 23, 25, 23, 23, 27, 23, 21, 19, 19, 21, 19, 17, 19, 17, 19, 17, 17, 15, 13, 11, 9, 11, 9, 60, 58, 54, 11, 9, 7, 30, 28
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| As explained in A138751, the map x->A007918(A138750(x))
is a natural generalization of the Collatz map to primes.
The only even prime p=2 is the only fixed point of this map,
and all odd primes seem to end up in the loop 7 -> 17 -> 11 -> 7,
after a number of steps given in the present sequence.
(It might have been more natural to count the number of steps
until a same number is reached for the second time.
Depending on which number among {2,7,11,17} is reached first,
this would increase the value of a(n) by 1,3,2 resp. 1.)
|
|
|
LINKS
| Georges Brougnard, Trajectory of 4499221.
Index entries for sequences related to 3x+1 (or Collatz) problem
|
|
|
EXAMPLE
| a(1)=a(4)=0 since prime(1)=2 and prime(4)=7
are by definition the values at which counting ends.
a(primepi(4499221))=63337 according to G.Brougnard, c.f. Link.
|
|
|
PROG
| (PARI) A138752(n, c=0) = { if( n==1 & 7==n=prime(n), 0, until( 7==n=nextprime( if( n%3==2, ceil(n/2), 2*n )), c++); c)}
|
|
|
CROSSREFS
| Cf. A124123, A138750, A138751, A138753.
Sequence in context: A176703 A160648 A124912 * A098689 A158984 A158417
Adjacent sequences: A138749 A138750 A138751 * A138753 A138754 A138755
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| M. F. Hasler (www.univ-ag.fr/~mhasler), Mar 28 2008
|
| |
|
|
