A127633 Pure numbers in the Collatz (3x+1) iteration that are not multiples of 3.

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

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 18.

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