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A086004 Primes which remain prime after one and after two and after three applications of the rotate-and-add operation of A086002. 5
12917, 12919, 18911, 18913, 22907, 24907, 26903, 28901, 1088063, 1288043, 1408031, 1428029, 1528019, 100083679, 100280419, 100283849, 100483847, 100692793, 100880413, 101080159, 101283839, 101683093, 101683663, 102080149 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

These are the primes of A086003 which in addition remain prime after one additional, third application of the rotate-and-add operation.

Note: Have not yet found any 4-Rotation Cycle Primes.

Conjecture 1: Rotation and addition of primes with even numbers of digits never yields a prime.

Conjecture 2: There are no 5-Rotation Cycle Primes.

[Conjecture 1 is true because rotation for even numbers of the form 10^k*a+b yields 10^k*b+a, so rotation-and-add yields (10^k+1)*(a+b), which obviously contains a divisor A000533. RJM, Sep 17 2009]

4-Rotation Cycle Primes exist and are listed in A261458. - Chai Wah Wu, Aug 20 2015

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

FORMULA

{p in A086003: p+rot(p) in A086003}.

EXAMPLE

a(1)=12917 is in the sequence because 2-fold rotate-and-add yields the prime 60659 as shown in A086003, and the third application yields 60659+59660 = 120319 which still is prime.

CROSSREFS

Cf. A086002, A086003.

Sequence in context: A212079 A162895 A256746 * A090887 A246890 A145333

Adjacent sequences:  A086001 A086002 A086003 * A086005 A086006 A086007

KEYWORD

base,nonn

AUTHOR

Chuck Seggelin (barkeep(AT)plastereddragon.com), Jul 07 2003

EXTENSIONS

Condensed by R. J. Mathar, Sep 17 2009

STATUS

approved

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Last modified October 16 16:18 EDT 2019. Contains 328101 sequences. (Running on oeis4.)