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Terms of A127928 that are prime in A006577.
3

%I #11 Mar 01 2020 08:20:41

%S 3,43,109,163,307,439,541,619,937,1069,1087,1297,1303,1321,1609,1621,

%T 1627,1657,1783,1861,2053,2251,2293,2311,2347,2647,2689,3067,3121,

%U 3319,3373,3457,3499,3511,3517,3607,3637,3769,4051,4057,4219,4363,4561,4723,4813,4903

%N Terms of A127928 that are prime in A006577.

%C Through a(9) the terms have the following number of 3x+1 problem steps: 7, 29, 113, 23, 37, 53, 43, 131, 173.

%H Amiram Eldar, <a href="/A127930/b127930.txt">Table of n, a(n) for n = 1..2000</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, pp. 194-201.

%F A127928 = numbers that are both pure hailstone (Collatz) and prime. A127930 = the subset having prime steps to reach 1; given the Collatz rule C(n) = {3n+1, n odd; n/2 if n is even}.

%e 3 is in the set A127930 since the iterative trajectory of 3 has 7 steps: (10, 5, 16, 8, 4, 2, 1) and 7 is prime.

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

%K nonn

%O 1,1

%A _Gary W. Adamson_, Feb 07 2007

%E More terms from _Amiram Eldar_, Feb 28 2020