A127928 -id:A127928 - cp's OEIS frontend

A127930 Terms of A127928 that are prime in A006577.

3, 43, 109, 163, 307, 439, 541, 619, 937, 1069, 1087, 1297, 1303, 1321, 1609, 1621, 1627, 1657, 1783, 1861, 2053, 2251, 2293, 2311, 2347, 2647, 2689, 3067, 3121, 3319, 3373, 3457, 3499, 3511, 3517, 3607, 3637, 3769, 4051, 4057, 4219, 4363, 4561, 4723, 4813, 4903

Offset: 1

Gary W. Adamson, Feb 07 2007

nonn

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

			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.

Amiram Eldar, Table of n, a(n) for n = 1..2000
Douglas J. Shaw, The Pure Numbers Generated by the Collatz Sequence, The Fibonacci Quarterly, Vol. 44, Number 3, August 2006, pp. 194-201.

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

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}.

More terms from Amiram Eldar, Feb 28 2020

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

Original entry on oeis.org

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

Gary W. Adamson, Feb 07 2007

nonn

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.

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

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.

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

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

More terms from Amiram Eldar, Feb 28 2020

cp's OEIS Frontend

A127930 Terms of A127928 that are prime in A006577.

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