A104646 - OEIS

%I #14 May 13 2013 01:54:08

%S 9,10,21,34,51,58,77,106,129,166,201,262,287,334,381,454,501,586,669,

%T 718,791,922,989,1082,1167,1282,1371,1486,1623,1754,1851,2018,2127,

%U 2326,2427,2638,2747,2974,3093,3274,3459,3694,3831,4034,4227,4534,4661,4894,5123,5366

%N Smallest semiprime equal to the sum of n distinct primes.

%C The sequence is monotonic for its first million terms.  Does there exist n with a(n) < a(n-1)? [_Charles R Greathouse IV_, Aug 24 2011]

%H Charles R Greathouse IV, <a href="/A104646/b104646.txt">Table of n, a(n) for n = 2..10000</a>

%e a(2) = 9 because 9 = 2+7=9 = 3*3;

%e a(3) = 10 because 10 = 2+3+5 = 2*5;

%e a(4) = 21 because 21 = 2+3+5+11 = 3*7.

%o (PARI) issemi(n)=bigomega(n)==2

%o a(n)={

%o     my(v=primes(n+3),s=sum(i=1,n+1,v[i]),m,t,t1);

%o     m=s+v[n+2]-5;

%o     forstep(i=n+1,1,-1,

%o         t=s-v[i];

%o         if(t >= m, break);

%o         if(issemi(t),return(t))

%o     );

%o     s+=v[n+2];

%o     m=s+v[n+3]-10;

%o     for(i=2,n+2,

%o         t=s-v[i];

%o         for(j=1,i-1,

%o             t1=t-v[j];

%o             if(t1 >= m, break);

%o             if(issemi(t1),m=t1)

%o         )

%o     );

%o     if(issemi(m), return(m));

%o     error("could not find a("n")")

%o }; \\ _Charles R Greathouse IV_, Aug 24 2011

%K nonn

%O 2,1

%A _Giovanni Teofilatto_, Apr 21 2005

%E a(6) corrected, a(7)-a(50) by _Charles R Greathouse IV_, Aug 24 2011