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
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
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