A127929 a(n) = A127928(n) mod 18.

3, 7, 1, 1, 7, 1, 7, 7, 1, 1, 7, 1, 1, 1, 7, 7, 1, 7, 1, 7, 7, 7, 7, 1, 1, 7, 7, 7, 1, 1, 1, 7, 7, 1, 7, 1, 7, 7, 7, 7, 1, 1, 1, 7, 1, 7, 1, 7, 1, 7, 7, 7, 7, 1, 7, 1, 7, 7, 7, 1, 1, 7, 7, 1, 7, 7, 1, 7, 1, 1, 7, 1, 7, 1, 1, 7, 1, 7, 1, 7, 1, 7, 7, 7, 7, 7, 1

Offset: 1

Author

Gary W. Adamson, Feb 07 2007

Keywords

• nonn

Comments

Aside from "3", all terms of A127928 must be 1 or 7 mod 18 (see A127928 for mod rules); but not all primes mod 1 or 7 are pure hailstone numbers. For example, the prime 61 == 7 mod 18 but 61 is impure. Conjecture: for large n, the numbers of 1 and 7 mod 18 terms are approximately equal.

Examples

			a(5) = 7 since A127928(5) = 43 and 43 == 7 mod 18.
		

Links

• 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, p. 194.

Crossrefs

Cf. A127928, A127930, A061641, A127633, A006577, A066903.

Formula

Pure hailstone (Collatz) numbers that are also prime (i.e. the set A127928), mod 18.

Extensions

More terms from Amiram Eldar, Feb 28 2020