login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A130142 Let f denote the map that replaces k by the concatenation of its proper divisors, written in decreasing order, each divisor being written in base 10 with its digits in reverse order. Then a(n) = first prime reached when starting at 2n+1 and iterating f. 5
1, 3, 5, 7, 3, 11, 13, 53, 17, 19, 73, 23, 5, 9343, 29, 31, 113, -1, 37, 313, 41, 43 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

If 2n+1 is 1 or a prime, set a(n) = 2n+1. If no prime is ever reached, set a(n) = -1.

LINKS

Table of n, a(n) for n=0..21.

EXAMPLE

n = 13: 2n+1 = 27 has proper divisors 3 and 9, so we get 93, which has proper divisors 3 and 31, so we get 133.

Then 133 has proper divisors 7 and 19, so we get 917.

Then 917 has proper divisors 7 and 131, so we get 1317.

Then 1317 has proper divisors 3 and 439, so we get 9343, a prime and a(13) = 9343.

From Sean A. Irvine, Sep 11 2009: (Start)

Proof chain for a(17). The following gives the argument to f at each step, followed by its factorization.

35 factors as 5 * 7.

75 has factors 3 * 5 * 5.

525153 has factors 3 * 193 * 907.

15057112727099753913 has factors 3 * 4463 * 17215189 * 65325353.

179719996575730910515106159846737337176838928854211713151146478934050745192125561494032705883138679506795913535235676554615981512719833136443 has factors 29 * 29 * 5546454298803948416569 * 8370112457804191610629 * 13338101723922940394396774098231 * 345111672681489292530961043464303237918570147336150469919363833

765...4892 (3249 digits) is divisible by 2, and hence all subsequent steps will be divisible by 2, therefore no prime is ever reached, therefore a(17)=-1. (End)

CROSSREFS

Cf. A130139, A130140, A130141, A120716.

Sequence in context: A100029 A099984 A130141 * A130139 A204938 A101088

Adjacent sequences:  A130139 A130140 A130141 * A130143 A130144 A130145

KEYWORD

base,more,sign

AUTHOR

Adam L. Buchsbaum (alb(AT)research.att.com), Jul 30 2007, Aug 01 2007

EXTENSIONS

The value of a(17) is currently unknown.

5 more terms (details for a(17) in example). Next term requires factoring a 1478-digit number. - Sean A. Irvine, Sep 11 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 22 22:37 EST 2014. Contains 252372 sequences.