A171619 Primes in A171490.

5, 7, 29, 67, 83, 109, 173, 239, 241, 251, 293, 313, 337, 367, 571, 613, 769, 821, 877, 941, 947, 1031, 1069, 1103, 1511, 1693, 1759, 1901, 2011

Offset: 1

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Dec 13 2009

Keywords

• nonn
• hard
• more

Comments

Terms of sequence are primes in growing order where smallest number of steps m to reach 1 in "3x+1" (or Collatz) problem is a prime too.

Examples

			(1) 1st Collatz sequence with 5=prime(3) steps starts with 5=prime(3): 5-16-8-4-2-1, gives a(1)=5.
(2) 1st Collatz sequence with 7=prime(4) steps starts with 3=prime(2): 3-10-5-16-8-4-2-1, gives a(2)=7.
(3) 1st Collatz sequence with 29=prime(10) steps starts with 43=prime(14): 43-130-65-196-98-49-148-74-37-112-56-28-14-7-22-11-34-17-52-26-13-40-20-10-5-16-8-4-2-1, gives a(3)=29.
(4) List of prime steps m for above a(n): 5, 3, 43, 167, 233, 41, 937, 14831, 9887, 7963, 73063, 45127, 78791, 225023, 6956969, 10998599, 126357223, 859130059, 2845683047, 322623647, 95592191, 8363817307, 28677246203, 38590505339, 35521451596571, 478672174364191, 1168778549494463, 6376392739978081, 103147916159472367.
		

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.
• Guenther J. Wirsching, The Dynamical System Generated by the 3n+1 Function, Springer-Verlag, Berlin, 1998.

Links

• Eric Roosendaal, 3x+1 Class Records
• Eric Weisstein's World of Mathematics, Collatz Problem

Crossrefs

Cf. A070905, A033491, A088975, A126727, A060565, A171490.

Extensions

Missing term a(7)=173 inserted by Georg Fischer, Oct 26 2022

a(23)-a(29) (using Eric Roosendaal's data) by Tyler Busby, Feb 11 2023