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A087054 Primes of the form pq + qr + rp where p, q and r are distinct primes. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

EXAMPLE

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).

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 *)

PROG

(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

(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

CROSSREFS

Cf. A087053 (numbers of the form pq+qr+rp).

Cf. A189759 (p*q*r for primes of this form).

Sequence in context: A104822 A198175 A238397 * A245650 A098711 A087053

Adjacent sequences:  A087051 A087052 A087053 * A087055 A087056 A087057

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Aug 07 2003

EXTENSIONS

Corrected by T. D. Noe, Apr 27 2011

STATUS

approved

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Last modified June 25 07:53 EDT 2019. Contains 324347 sequences. (Running on oeis4.)