|
| |
|
|
A127633
|
|
Pure numbers in the Collatz (3x+1) iteration that are not multiples of 3.
|
|
5
|
|
|
|
1, 7, 19, 25, 37, 43, 55, 73, 79, 97, 109, 115, 127, 133, 145, 151, 163, 169, 181, 187, 199, 217, 223, 235, 241, 259, 271, 277, 289, 295, 307, 313, 331, 343, 349, 361, 367, 379, 385, 397, 403, 421, 439, 451, 457, 469, 475, 487, 493, 505, 511, 523, 529, 541
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
The sequence is a list of pure numbers not congruent to 0 mod 3. The remaining pure numbers are congruent to 1 or 7 mod l8.
After computing all a(n) < 10^9, the ratio a(n)/n appears to be converging to 10.101... Hence it appears that the numbers in this sequence have a density of about 99/1000. - T. D. Noe, Oct 12 2007
|
|
|
REFERENCES
|
Douglas J. Shaw, "The Pure Numbers Generated by the Collatz Sequence", The Fibonacci Quarterly, Vol. 44, Number 3, August 2006, p. 194.
|
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=1..10000
|
|
|
FORMULA
|
A positive integer n is pure if its entire tree of preimages under the Collatz function C is greater than or equal to it; otherwise n is impure [Shaw, p. 195]. For n a positive integer, the function C is defined by C(n) = {3n+1, n odd; n/2, n even}.
|
|
|
CROSSREFS
|
Cf. A061641
Sequence in context: A176182 A065749 A032642 * A055246 A003282 A006063
Adjacent sequences: A127630 A127631 A127632 * A127634 A127635 A127636
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Gary W. Adamson, Jan 20 2007
|
|
|
EXTENSIONS
|
Edited by N. J. A. Sloane and T. D. Noe, Oct 16 2007
|
|
|
STATUS
|
approved
|
| |
|
|
