A127930 - OEIS

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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

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OFFSET

1,1

COMMENTS

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

LINKS

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.

FORMULA

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}.

EXAMPLE

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.

CROSSREFS

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

Sequence in context: A142184 A199348 A002551 * A062647 A003525 A042661

Adjacent sequences: A127927 A127928 A127929 * A127931 A127932 A127933

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Feb 07 2007

EXTENSIONS

More terms from Amiram Eldar, Feb 28 2020

STATUS

approved