%I #22 Sep 08 2022 08:45:46
%S 1427,2857,5717,11437,22877,45757,183037,366077,732157,23429117,
%T 1499463677,191931351037,98268851732477,393075406929917,
%U 6289206510878717,50313652087029757,100627304174059517,201254608348119037,12880294934279618557,422061504406474540974077
%N Primes in the chain of repeated application of x>2*x+3, starting at x=1427.
%C All primes created that way are congruent to 712 (mod 715).
%C Numbers in the chain may not be prime, for example 2*45757 + 3 = 91517.
%C The first primes congruent to 712 (mod 715) that are missed by the chain are 10007, 15727 and 18587.
%C 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
%H Vincenzo Librandi, <a href="/A163589/b163589.txt">Table of n, a(n) for n = 1..46</a>
%e p = 1427, a prime, begins the sequence;
%e 2*1427 + 3 = 2857 is prime and thus is a term.
%e 2*2857 + 3 = 5717 is prime and thus is a term.
%p 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
%t Select[NestList[2 # + 3 &, 1427, 30], PrimeQ] (* _Vincenzo Librandi_, May 14 2013 *)
%o (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
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Aug 01 2009
%E Definition corrected by _R. J. Mathar_, Aug 01 2009
