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A245441 a(1)=3, then a(n) = smallest odd k > Ceiling(a(n-1)/2) such that k*2^n-1 is prime.

%I A245441 #25 Apr 25 2016 11:50:03
%S A245441 3,3,3,3,7,17,13,27,25,15,25,23,21,15,9,17,15,21,51,35,19,33,25,39,57,
%T A245441 57,81,45,45,213,111,57,31,131,99,83,45,27,25,107,55,33,33,35,67,141,
%U A245441 91,89,69,41,129,89,147,101,195,129,79,77,45,77,69,53,61
%N A245441 a(1)=3, then a(n) = smallest odd k > Ceiling(a(n-1)/2) such that k*2^n-1 is prime.
%C A245441 A126715(n) = smallest odd k such that k*2^n-1 is prime, the primes are not always in increasing order.
%C A245441 Here the primes k*2^n-1 are always in increasing order.
%C A245441 The ratio sum_{1..N}a(n)/sum_{1..N}n is near 2*log(2) as N increases.
%C A245441 The ratio a(n)/n is always < 8 for n from 1 to 6000.
%H A245441 Pierre CAMI, <a href="/A245441/b245441.txt">Table of n, a(n) for n = 1..6000</a>
%e A245441 3*2^1-1 = 5 is prime, a(1)=3 by definition.
%e A245441 3*2^2-1 = 11 is prime, 3 > 3/2 so a(2) = 3.
%e A245441 3*2^3-1 = 23 is prime, so a(3) = 3.
%e A245441 3*2^4-1 = 47 is prime, so a(4) = 3.
%e A245441 3*2^5-1 = 95 is composite.
%e A245441 5*2^5-1 = 159 is composite.
%e A245441 7*2^5-1 = 223 is prime so a(5) = 7.
%o A245441 (PFGW & SCRIPT)
%o A245441 SCRIPT
%o A245441 DIM j,-1
%o A245441 DIM n,0
%o A245441 DIMS t
%o A245441 OPENFILEOUT myf,a(n).txt
%o A245441 LABEL loop1
%o A245441 SET n,n+1
%o A245441 IF n>6000 THEN END
%o A245441 LABEL loop2
%o A245441 SET j,j+2
%o A245441 SETS t,%d,%d\,;n;j
%o A245441 PRP j*2^n-1,t
%o A245441 IF ISPRP THEN GOTO a
%o A245441 GOTO loop2
%o A245441 LABEL a
%o A245441 WRITE myf,t
%o A245441 SET j,j/2
%o A245441 IF j%2==0 THEN SET j,j+1
%o A245441 GOTO loop1
%o A245441 (PARI) a=[3]; for(n=2, 100, k=floor(a[n-1]/2)+2; if(k%2==0, k++); t=2^n; while(!isprime(k*t-1), k+=2); a=concat(a, k)); a \\ _Colin Barker_, Jul 22 2014
%Y A245441 Cf. A126715.
%K A245441 nonn
%O A245441 1,1
%A A245441 _Pierre CAMI_, Jul 22 2014