A127929 - OEIS

%I #13 Feb 28 2020 03:36:07

%S 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,

%T 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,

%U 1,1,7,1,7,1,1,7,1,7,1,7,1,7,7,7,7,7,1

%N a(n) = A127928(n) mod 18.

%C 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.

%H Amiram Eldar, <a href="/A127929/b127929.txt">Table of n, a(n) for n = 1..10000</a>

%H Douglas J. Shaw, <a href="http://www.fq.math.ca/Papers1/44-3/quartshaw03_2006.pdf">The Pure Numbers Generated by the Collatz Sequence</a>, The Fibonacci Quarterly, Vol. 44, Number 3, August 2006, p. 194.

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

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

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

%K nonn

%O 1,1

%A _Gary W. Adamson_, Feb 07 2007

%E More terms from _Amiram Eldar_, Feb 28 2020