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%I #8 Oct 08 2012 22:41:50
%S 5,53,67,89,113,131,173,211,251,293,307,337,379,409,449,487,491,499,
%T 631,683,701,727,751,769,787,919,941,953,991,1009,1039,1051,1063,1117,
%U 1193,1259,1399,1459,1471,1499,1511,1567,1627,1697,1709,1733,1759,1787,1801
%N Primes which are the average of two successive semiprimes.
%H Zak Seidov, <a href="/A103654/b103654.txt">Table of n, a(n) for n = 1..10000</a>
%F p=(q+r)/2, where q<p and r>p are two successive semiprimes closest to p.
%e a(3)=67 because 65 and 69 are two successive semiprimes closest to 67 and 67=(65+69)/2;a(333)=22679 because 22677 and 22691 are two successive semiprimes closest to 22679 and 22679=(22677+22681)/2.
%o (PARI) list(lim)=my(v=List(),u=v,t,lim2=lim+log(lim)^2);forprime(p=2,sqrt(lim2),t=p;forprime(q=p,lim2\t,listput(v,t*q)));v=vecsort(Vec(v));for(i=2,#v,t=(v[i]+v[i-1])/2;if(denominator(t)==1&&isprime(t),if(t>lim,break,listput(u,t))));Vec(u) \\ _Charles R Greathouse IV_, Oct 08 2012
%Y Indices of these primes: A103655. Primes: A000040, semiprimes: A001358, number of primes between successive semiprimes: A088700, number of semiprimes between two successive primes: A103668.
%Y Cf. A000040, A088700, A103655, A001358, A103668, A103669.
%K nonn
%O 1,1
%A _Zak Seidov_, Feb 12 2005
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