A087054 Primes of the form pq + qr + rp where p, q and r are distinct primes.
31, 41, 59, 61, 71, 101, 103, 113, 131, 151, 167, 191, 199, 211, 227, 239, 241, 251, 263, 269, 271, 281, 293, 311, 331, 347, 359, 383, 401, 419, 421, 431, 439, 461, 467, 479, 487, 491, 503, 521, 541, 563, 571, 587, 599, 607, 617, 631, 641, 647, 653, 661, 691
Offset: 1
Keywords
Examples
A003415(2*3*19)=2*3+3*19+19*2=101=A000040(26), therefore 101 is a term (but also A003415(2*5*13)=2*5+5*13+13*2=101).
Links
- T. D. Noe, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
sumProd[p_,q_,r_]:=p*q+p*r+q*r; pqrPrimes[nn_] := Module[{p=Prime[Range[PrimePi[(nn-6)/5]+1]],i,j,k,n}, Union[Reap[i=0; While[i++; sumProd[p[[i]],p[[i+1]],p[[i+2]]] <= nn, j=i; While[j++; sumProd[p[[i]],p[[j]],p[[j+1]]] <= nn, k=j; While[k++; n=sumProd[p[[i]],p[[j]],p[[k]]]; n <= nn, If[PrimeQ[n], Sow[n]]]]]][[2,1]]]]; pqrPrimes[1000] (* T. D. Noe, Apr 27 2011 *) nn=100;Take[Select[Union[Total[Times@@@Subsets[#,{2}]]&/@Subsets[ Prime[ Range[ nn]],{3}]],PrimeQ],nn] (* Harvey P. Dale, Jan 08 2013 *) -
PARI
list(lim)=my(v=List()); forprime(r=5, (lim-6)\5, forprime(q=3, min((lim-2*r)\(r+2), r-2), my(S=q+r, P=q*r); forprime(p=2, min((lim-P)\S, q-1), isprime(p*S+P) && listput(v,p*S+P)))); Set(v) \\ Charles R Greathouse IV, Feb 26 2014
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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(isprime(n))))); 0 \\ Charles R Greathouse IV, Feb 26 2014
Extensions
Corrected by T. D. Noe, Apr 27 2011