A104646 Smallest semiprime equal to the sum of n distinct primes.

9, 10, 21, 34, 51, 58, 77, 106, 129, 166, 201, 262, 287, 334, 381, 454, 501, 586, 669, 718, 791, 922, 989, 1082, 1167, 1282, 1371, 1486, 1623, 1754, 1851, 2018, 2127, 2326, 2427, 2638, 2747, 2974, 3093, 3274, 3459, 3694, 3831, 4034, 4227, 4534, 4661, 4894, 5123, 5366

Offset

2,1

Comments

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]

Links

Charles R Greathouse IV, Table of n, a(n) for n = 2..10000

Example

a(2) = 9 because 9 = 2+7=9 = 3*3;
a(3) = 10 because 10 = 2+3+5 = 2*5;
a(4) = 21 because 21 = 2+3+5+11 = 3*7.

Prog

(PARI) issemi(n)=bigomega(n)==2
a(n)={
    my(v=primes(n+3), s=sum(i=1, n+1, v[i]), m, t, t1);
    m=s+v[n+2]-5;
    forstep(i=n+1, 1, -1,
        t=s-v[i];
        if(t >= m, break);
        if(issemi(t), return(t))
    );
    s+=v[n+2];
    m=s+v[n+3]-10;
    for(i=2, n+2,
        t=s-v[i];
        for(j=1, i-1,
            t1=t-v[j];
            if(t1 >= m, break);
            if(issemi(t1), m=t1)
        )
    );
    if(issemi(m), return(m));
    error("could not find a("n")")
}; \\ Charles R Greathouse IV, Aug 24 2011

Crossrefs

Sequence in context: A178350 A085949 A102238 * A214425 A260184 A109463

Adjacent sequences: A104643 A104644 A104645 * A104647 A104648 A104649

Keyword

nonn

Author

Giovanni Teofilatto, Apr 21 2005

Extensions

a(6) corrected, a(7)-a(50) by Charles R Greathouse IV, Aug 24 2011

Status

approved