A127929 -id:A127929 - cp's OEIS frontend

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, 1009, 1033, 1051, 1069, 1087, 1117

Offset: 1

Gary W. Adamson, Feb 07 2007

nonn

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.

			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).

Amiram Eldar, 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, pp. 194-201.

Cf. A127929, A127930, A061641, A127633, A066903.

More terms from Amiram Eldar, Feb 28 2020

cp's OEIS Frontend

A127928 Pure hailstone primes.

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