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Revision History for A175177

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A175177

Conjectured number of numbers for which the iteration x -> phi(x) + 1 terminates at prime(n). Cardinality of rooted tree T_p (where p is n-th prime) in Karpenko's book.
(history; published version)

#26 by Peter Luschny at Mon Sep 25 05:43:11 EDT 2017

STATUS

proposed

approved

#25 by Michel Marcus at Mon Sep 25 02:57:12 EDT 2017

STATUS

editing

proposed

Discussion

Mon Sep 25

05:43

Peter Luschny: OK, from reading Karpenko I think the given numbers are proved.
But I did not study the subject thoroughly and agree to be cautious.

#24 by Michel Marcus at Mon Sep 25 02:56:51 EDT 2017

REFERENCES

A. S. Karpenko A.S. 2006. , Lukasiewicz's Logics and Prime Numbers , (English translation), 2006. See Table 2 on p.125 ff.

A. S. Karpenko A.S. 2000. , Lukasiewicz's Logics and Prime Numbers , (Russian), 2000.

STATUS

proposed

editing

#23 by Peter Luschny at Sun Sep 24 16:23:52 EDT 2017

STATUS

editing

proposed

Discussion

Sun Sep 24

19:57

Hugo Pfoertner: Because my computation was only experimental moving the  limits far beyond the last occurrence of a contribution to the counts. If Karpenko or someone else provides a proof of bounds, the "conjectured" can be removed.

#22 by Peter Luschny at Sun Sep 24 16:22:32 EDT 2017

EXAMPLE

a(3) = 4 because x = { 5, 8, 10, 12 } are the 4 numbers from which the iteration x -> phi(x) + 1 terminates at prime(3) = 5.

a(4) = 8 because x = { 7, 9, 14, 15, 16, 18, 20, 24, 30 } are the 9 numbers from which the iteration x -> phi(x) + 1 terminates at prime(4) = 7.

STATUS

reviewed

editing

Discussion

Sun Sep 24

16:23

Peter Luschny: Hugo, why do you say 'Conjectured '?

#21 by Joerg Arndt at Sun Sep 24 06:09:29 EDT 2017

STATUS

proposed

reviewed

#20 by Joerg Arndt at Sun Sep 24 06:09:23 EDT 2017

STATUS

editing

proposed

#19 by Joerg Arndt at Sun Sep 24 06:09:17 EDT 2017

EXTENSIONS

Name clarified by Hugo Pfoertner, Sep 23 2017

STATUS

proposed

editing

#18 by Hugo Pfoertner at Sun Sep 24 05:46:54 EDT 2017

STATUS

editing

proposed

#17 by Hugo Pfoertner at Sun Sep 24 05:44:52 EDT 2017

NAME

aConjectured number of numbers for which the iteration x -> phi(x) + 1 terminates at prime(n) = cardinality . Cardinality of rooted tree T_p (where p is n-th prime) in Karpenko's book.

COMMENTS

Also conjectured number of numbers for which the iteration x -> phi(x) + 1 terminates at prime(n). - Hugo Pfoertner, Sep 23 2017

STATUS

proposed

editing

Discussion

Sun Sep 24

05:46

Hugo Pfoertner: Peter, Joerg, I've now moved my comment into the title, but leaving the old as second meaning.