

A127928


Pure hailstone primes.


3



3, 7, 19, 37, 43, 73, 79, 97, 109, 127, 151, 163, 181, 199, 223, 241, 271, 277, 307, 313, 331, 349, 367, 379, 397, 421, 439, 457, 487, 523, 541, 547, 601, 613, 619, 631, 673, 691, 709, 727, 757, 811, 829, 853, 883, 907, 937, 997
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OFFSET

1,1


COMMENTS

In other words, pure hailstone numbers that are also primes (primes in A061641).
Impure hailstone numbers occur in the trajectories of smaller numbers, using the definition C(n) = (3n+1, n odd; n/2 if n is even). The set of pure hailstone numbers and the subset of pure, prime hailstone numbers; may be obtained through a process of elimination. The rules [cf. Shaw, p. 199] for A127928(n>1) force the terms to be == 1 or 7 mod 18; but not all primes mod 1 or 7 are in A127928. (e.g. 61 == 7 mod 18 and is prime but is not a pure hailstone number).
Shaw, p. 199: If n == 0, 3, 6, 9, 12 or 15 mod 18, then n is pure, but only 3 is prime. If n == 2, 4, 5, 8, 10, 11, 13, 14, 16 or 17 mod 18, then n is impure. If n == 1 or 7 mod 18, then n may be pure or impure.


LINKS

Table of n, a(n) for n=1..48.
Douglas J. Shaw, The Pure Numbers Generated by the Collatz Sequence, The Fibonacci Quarterly, Vol. 44, Number 3, August 2006, pp. 194201.


EXAMPLE

3 is a pure hailstone (Collatz) number since it does not appear in the orbit of 1 or 2, but 5 is impure since the iterative trajectory of 3 = (10, 5, 16, 8, 4, 2, 1).


CROSSREFS

Cf. A127929, A127930, A061641, A127633, A066903.
Sequence in context: A268065 A049490 A112391 * A298125 A047025 A222465
Adjacent sequences: A127925 A127926 A127927 * A127929 A127930 A127931


KEYWORD

nonn


AUTHOR

Gary W. Adamson, Feb 07 2007


STATUS

approved



