|
| |
|
|
A086004
|
|
Primes which remain prime after one and after two and after three applications of the rotate-and-add operation of A086002.
|
|
2
| |
|
|
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; 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]
|
|
|
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: A158918 A185885 A162895 * A090887 A145333 A190468
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 (mathar(AT)strw.leidenuniv.nl), Sep 17 2009
|
| |
|
|
