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Search: id:A086004
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| A086004 |
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Primes which remain prime after one and after two and after three applications of the rotate-and-add operation of A086002. |
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+0
3
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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]
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FORMULA
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{p in A086003: p+rot(p) in A086003}.
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EXAMPLE
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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.
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CROSSREFS
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Cf. A086002, A086003.
Sequence in context: A031805 A158918 A162895 this_sequence A090887 A145333 A028385
Adjacent sequences: A086001 A086002 A086003 this_sequence A086005 A086006 A086007
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KEYWORD
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base,nonn
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AUTHOR
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Chuck Seggelin (barkeep(AT)plastereddragon.com), Jul 07 2003
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EXTENSIONS
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Condensed by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 17 2009
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