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

Author

Gary W. Adamson, Jan 20 2007

Keywords

• nonn

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.

Crossrefs

Cf. A061641.

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}.

Extensions

Edited by N. J. A. Sloane and T. D. Noe, Oct 16 2007