A171490 Numbers for which the smallest number of steps to reach 1 in "3x+1" (or Collatz) problem is a prime.

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

Offset: 1

Author

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

Keywords

• nonn
• changed

Comments

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

Examples

			1st Collatz sequence with a(1)=1 step starts with 2=prime(1): 2-1;
1st Collatz sequence with a(3)=7 steps starts with 3=prime(2): 3-10-5-16-8-4-2-1;
prime(6)=13 has Collatz sequence with 9 steps: 13-40-20-10-5-16-8-4-2-1, so has the smaller composite 12 < 13: 12-6-3-10-5-16-8-4-2-1 => 9 not a term of sequence;
1st Collatz sequence with a(5)=14 steps starts with 11=prime(5): 11-34-17-52-26-13-40-20-10-5-16-8-4-2-1.
		

References

• R. K. Guy, "Collatz's Sequence" in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 215-218, 1994
• Clifford A. Pickover, Wonders of Numbers, Oxford University Press, pp. 116-118, 2001

Links

• J. C. Lagarias, The 3x+1 Problem and its Generalizations, Amer. Math. Monthly 92, 3-23, 1985

Crossrefs

Cf. A070905, A033491, A088975, A126727, A060565

Extensions

Terms > 187 from R. J. Mathar, Nov 01 2010

Name edited by Michel Marcus, Jul 07 2018