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Consider the least k such that prime(k) > n*composite(k). Sequence gives prime(k).
1

%I #7 Dec 05 2013 19:56:48

%S 11,53,173,521,1523,4327,11579,31469,85411,229547,614477,1640461,

%T 4393369,11806297,31656553,84979847,228346229,614582509,1654328267,

%U 4457160931,12016414601,32419200013,87508870037,236325429049,638490906857,1725782162981,4666340800001

%N Consider the least k such that prime(k) > n*composite(k). Sequence gives prime(k).

%C a(n) = prime(A073459(n)).

%e a(2) = 53 as 53 > 2*26 where 53 and 26 are respectively the 16th prime and composite numbers.

%o (PARI) nextcomposite(k)=if(k<3,4,if(isprime(k),k+1,k));

%o (PARI) p=2;q=4;for(n=1,19, while(p<=n*q,p=nextprime(p+1);q=nextcomposite(q+1));print1(p,","));

%Y Cf. A002808, A000040, A073459, A125075.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Apr 19 2004

%E Terms a(4) to a(19) and PARI code from _Klaus Brockhaus_, Apr 26 2004

%E Terms a(20) to a(23) from _Klaus Brockhaus_, Nov 19 2006

%E More terms from _David Wasserman_, Apr 20 2007