A163589 Primes in the chain of repeated application of x->2*x+3, starting at x=1427.

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

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

Vincenzo Librandi, Table of n, a(n) for n = 1..46

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

Select[NestList[2 # + 3 &, 1427, 30], PrimeQ] (* Vincenzo Librandi, May 14 2013 *)

Prog

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

Crossrefs

Sequence in context: A183780 A068572 A236897 * A250582 A260283 A156853

Adjacent sequences: A163586 A163587 A163588 * A163590 A163591 A163592

Keyword

nonn,easy

Author

Vincenzo Librandi, Aug 01 2009

Extensions

Definition corrected by R. J. Mathar, Aug 01 2009

Status

approved