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A171619 Primes in A171490. 0
5, 7, 29, 67, 83, 109, 239, 241, 251, 293, 313, 337, 367, 571, 613, 769, 821, 877, 941, 947, 1031 (list; graph; refs; listen; history; text; internal format)
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..21.

EXAMPLE

(1) 1st Collatz sequence with 5=prime(3) steps starts with 5=prime(3): 5-16-8-4-2-1, gives a(1)=7

(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, 14831, 9887, 7963, 73063, 45127, 78791, 225023, 6956969, 10998599, 126357223, 859130059, 2845683047, 322623647, 95592191, 8363817307

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

hard,nonn

AUTHOR

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

STATUS

approved

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Last modified September 19 11:31 EDT 2021. Contains 347556 sequences. (Running on oeis4.)