A238397 - OEIS

%I #10 Feb 27 2014 14:40:34

%S 31,41,59,61,71,87,91,101,103,113,119,121,129,131,143,151,161,167,171,

%T 185,191,199,211,213,215,221,227,239,241,243,247,251,263,269,271,275,

%U 281,293,297,299,301,311,321,327,331,339,341,343,347,355

%N Numbers of the form pq + qr + rp where p, q and r are distinct primes (sorted sequence without duplicates).

%C Numbers of the form e2(p, q, r) for distinct primes p, q, r, where e2 is the elementary symmetric polynomial of degree 2. Other sequences are obtained with different numbers of distinct primes and degrees: A000040 for 1 prime, A038609 and A006881 for 2 primes, A124867, this sequence, and A007304 for 3 primes. The 4-prime sequences are not presently in the OEIS with the exception of A046386. - _Charles R Greathouse IV_, Feb 26 2014

%H Jean-François Alcover, <a href="/A238397/b238397.txt">Table of n, a(n) for n = 1..1000</a>

%e 71 = 3*5 + 5*7 + 7*3 = 2*3 + 3*13 + 13*2 is in the sequence (only once, though 2 solutions exist).

%t terms = 50; dm (* initial number of primes *) = 10; f[p_, q_, r_] := p*q + q*r + r*p; Clear[A238397]; A238397[m_] := A238397[m] = Take[u = Union[f @@@ Subsets[Prime /@ Range[m], {3}]], Min[Length[u], terms]]; A238397[dm]; A238397[m = 2*dm]; While[Print["m = ", m]; A238397[m] != A238397[m - dm], m = m + dm]; A238397[m]

%o (PARI) is(n)=forprime(r=(sqrtint(3*n-3)+5)\3, (n-6)\5, forprime(q= sqrtint(r^2+n)-r+1, min((n-2*r)\(r+2), r-2), if((n-q*r)%(q+r)==0 && isprime((n-q*r)/(q+r)), return(1)))); 0 \\ _Charles R Greathouse IV_, Feb 26 2014

%o (PARI) list(n)=my(v=List()); forprime(r=5, (n-6)\5, forprime(q=3, min((n-2*r)\(r+2), r-2), my(S=q+r, P=q*r); forprime(p=2, min((n-P)\S, q-1), listput(v, p*S+P)))); Set(v) \\ _Charles R Greathouse IV_, Feb 26 2014

%Y Cf. A087053, A087054.

%K nonn

%O 1,1

%A _Jean-François Alcover_, Feb 26 2014