

A171490


Numbers for which the smallest number of steps to reach 1 in "3x+1" (or Collatz) problem is a prime.


1



1, 5, 7, 12, 14, 16, 29, 51, 56, 58, 60, 64, 65, 67, 74, 75, 78, 83, 87, 90, 100, 102, 104, 106, 109, 115, 118, 119, 122, 128, 130, 132, 134, 141, 142, 147, 161, 166, 173, 176, 187, 188, 200, 212, 219, 221, 231, 234, 239, 241, 251, 259, 264, 293, 313, 314, 316
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OFFSET

1,2


COMMENTS

Positions of primes in A033491. [R. J. Mathar, Nov 01 2010]


REFERENCES

R. K. Guy, "Collatz's Sequence" in Unsolved Problems in Number Theory, 2nd ed. New York: SpringerVerlag, pp. 215218, 1994
Clifford A. Pickover, Wonders of Numbers, Oxford University Press, pp. 116118, 2001


LINKS

Table of n, a(n) for n=1..57.
J. C. Lagarias, The 3x+1 Problem and its Generalizations, Amer. Math. Monthly 92, 323, 1985


EXAMPLE

1st Collatz sequence with a(1)=1 step starts with 2=prime(1): 21;
1st Collatz sequence with a(3)=7 steps starts with 3=prime(2): 3105168421;
prime(6)=13 has Collatz sequence with 9 steps: 134020105168421, so has the smaller composite 12 < 13: 1263105168421 => 9 not a term of sequence;
1st Collatz sequence with a(5)=14 steps starts with 11=prime(5): 1134175226134020105168421.


CROSSREFS

Cf. A070905, A033491, A088975, A126727, A060565
Sequence in context: A086255 A306513 A286901 * A047382 A314301 A314302
Adjacent sequences: A171487 A171488 A171489 * A171491 A171492 A171493


KEYWORD

nonn


AUTHOR

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Dec 10 2009


EXTENSIONS

Terms > 187 from R. J. Mathar, Nov 01 2010
Name edited by Michel Marcus, Jul 07 2018


STATUS

approved



