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A058048 For each prime P consider the generalized Collatz sequence of each integer N > 1 defined by c(0) = N, c(m+1) = c(m) * P + 1 if F > P, else c(m+1) = c(m) / F, where F is the smallest factor of c(m), until the sequence cycles. If all c(i) > 1 for some starting number N then P belongs to the sequence (and vice versa). 1
2, 11, 13, 17, 19, 23, 31, 37, 43, 47, 53, 59, 61, 67, 71, 73, 83, 97, 101, 103, 113, 131, 137, 139, 151, 163, 167, 173, 181, 193, 197, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 313, 331, 347, 353, 367, 373, 379, 383, 389, 401 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Missing primes are as yet only conjectures. Jeff Heleen checked the primes < 1000 and start points up to 10000000 (see Prime Puzzle 114 and example below). P=3 is the ordinary Collatz problem.

REFERENCES

Jerash University Journal 2000-2001

LINKS

Table of n, a(n) for n=1..56.

Randall L. Rathbun, Discussi on of this sequence

C. Rivera, Prime Puzzle 114

EXAMPLE

With P=11 and c(0)=17 then {c(m)} is 17, 188, 94, 47, 518, 37, 408, 68, 34, 17,...

CROSSREFS

Prime complement of A058047. Cf. A057446, A057216, A057534, A057614, A058047.

Sequence in context: A137238 A048521 A172071 * A241659 A038915 A166849

Adjacent sequences:  A058045 A058046 A058047 * A058049 A058050 A058051

KEYWORD

nonn

AUTHOR

Murad A. AlDamen (Divisibility(AT)yahoo.com), Nov 17 2000

EXTENSIONS

Edited by Henry Bottomley, Jun 14 2002

Corrected by T. D. Noe, Oct 25 2006

STATUS

approved

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Last modified April 22 10:29 EDT 2019. Contains 322330 sequences. (Running on oeis4.)