

A127633


Pure numbers in the Collatz (3x+1) iteration that are not multiples of 3.


6



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
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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


LINKS

T. D. Noe, Table of n, a(n) for n=1..10000
Douglas J. Shaw, The Pure Numbers Generated by the Collatz Sequence, The Fibonacci Quarterly, Vol. 44, Number 3, August 2006, p. 194.


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: A292349 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



