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Revision History for A007755

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Showing entries 1-10 | older changes
Smallest number m such that the trajectory of m under iteration of Euler's totient function phi(n) [A000010] contains exactly n distinct numbers, including m and the fixed point.
(history; published version)
#49 by Charles R Greathouse IV at Tue Mar 26 23:41:00 EDT 2019
STATUS

editing

approved

#48 by Charles R Greathouse IV at Tue Mar 26 23:40:57 EDT 2019
COMMENTS

Shapiro mentions on page 30 of his paper the conjecture that a(n) is prime for each n > 1, but a(13) is composite and so the conjecture fails. [_- _Charles R Greathouse IV_, Oct 28 2011]

STATUS

approved

editing

#47 by Joerg Arndt at Sun Jun 26 06:16:59 EDT 2016
STATUS

proposed

approved

#46 by Michel Marcus at Sun Jun 26 05:12:24 EDT 2016
STATUS

editing

proposed

#45 by Michel Marcus at Sun Jun 26 05:12:18 EDT 2016
COMMENTS

Shapiro shows that the smallest number is greater the than 2^(n-1). Catlin shows that if a(n) is odd and composite, then its factors are among the a(k), k < n. For example a(12) = a(5) a(8). There is a conjecture that all terms of this sequence are odd. - T. D. Noe, Mar 08 2004

STATUS

approved

editing

#44 by R. J. Mathar at Fri Aug 28 12:36:52 EDT 2015
STATUS

editing

approved

#43 by R. J. Mathar at Fri Aug 28 12:36:46 EDT 2015
LINKS

T. D. Noe, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL11/Noe/noe080107.html">Primes in classes of the iterated totient function</a>, JIS 11 (2008) 08.1.2

STATUS

approved

editing

#42 by Michel Marcus at Tue Jan 06 03:59:48 EST 2015
STATUS

editing

approved

#41 by Michel Marcus at Tue Jan 06 03:59:43 EST 2015
COMMENTS

The indices of odd prime terms are given by n=A136040(k)+2 for k=1,2,3,.... - _T. D. Noe, _, Dec 14 2007

STATUS

reviewed

editing

#40 by Joerg Arndt at Tue Jan 06 03:51:12 EST 2015
STATUS

proposed

reviewed