

A163589


Primes in the chain of repeated application of x>2*x+3, starting at x=1427.


4



1427, 2857, 5717, 11437, 22877, 45757, 183037, 366077, 732157, 23429117, 1499463677, 191931351037, 98268851732477, 393075406929917, 6289206510878717, 50313652087029757, 100627304174059517, 201254608348119037, 12880294934279618557, 422061504406474540974077
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OFFSET

1,1


COMMENTS

All primes created that way are congruent to 712 (mod 715).
Numbers in the chain may not be prime, for example 2*45757 + 3 = 91517.
The first primes congruent to 712 (mod 715) that are missed by the chain are 10007, 15727 and 18587.
On the first comment: it is easy to see that these primes are of the form 715*2^k  3.  Bruno Berselli, May 14 2013


LINKS



EXAMPLE

p = 1427, a prime, begins the sequence;
2*1427 + 3 = 2857 is prime and thus is a term.
2*2857 + 3 = 5717 is prime and thus is a term.


MAPLE

x := 1427 ; for i from 1 to 80 do if isprime(x) then printf("%d, ", x) ; end if; x := 2*x+3 ; end do: # R. J. Mathar, Aug 02 2009


MATHEMATICA



PROG

(Magma) x:=1427; a:=[n eq 1 select x else 2*Self(n1)+3: n in [1..100]]; [a[i]: i in [1..#a]  IsPrime(a[i])]; // Bruno Berselli, May 14 2013


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



