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

1,1

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.

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

Table of n, a(n) for n=1..29.

Eric Roosendaal, 3x+1 Class Records

Eric Weisstein's World of Mathematics, Collatz Problem

Example

(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.

Crossrefs

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

Sequence in context: A280926 A070153 A293943 * A153411 A081630 A307532

Adjacent sequences: A171616 A171617 A171618 * A171620 A171621 A171622

Keyword

nonn,hard,more

Author

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

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

Status

approved