

A086004


Primes which remain prime after one and after two and after three applications of the rotateandadd 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
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OFFSET

1,1


COMMENTS

These are the primes of A086003 which in addition remain prime after one additional, third application of the rotateandadd operation.
Note: Have not yet found any 4Rotation Cycle Primes.
Conjecture 1: Rotation and addition of primes with even numbers of digits never yields a prime.
Conjecture 2: There are no 5Rotation Cycle Primes.
[Conjecture 1 is true because rotation for even numbers of the form 10^k*a+b yields 10^k*b+a, so rotationandadd yields (10^k+1)*(a+b), which obviously contains a divisor A000533. RJM, Sep 17 2009]
4Rotation 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 2fold rotateandadd 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



