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 A163589 Primes in the chain of repeated application of x->2*x+3, starting at x=1427. 4

%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(n-1)+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

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Last modified August 14 12:42 EDT 2024. Contains 375164 sequences. (Running on oeis4.)