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A290435 Semiprimes of the form pq where p < q and p+q+1 is prime. 2

%I

%S 21,35,39,55,57,65,77,85,111,115,129,155,161,185,187,201,203,205,209,

%T 221,235,237,265,291,299,305,309,319,323,327,335,341,365,371,377,381,

%U 391,413,415,437,451,485,489,493,497,505,515,517,535,579,611,623,649,655

%N Semiprimes of the form pq where p < q and p+q+1 is prime.

%C Squarefree terms of A290434.

%C All terms are odd.

%C A286842(a(n)) = 1 for all n.

%H Chai Wah Wu, <a href="/A290435/b290435.txt">Table of n, a(n) for n = 1..10000</a>

%e 655 = 5*131 and 5+131+1 is prime, so 655 is a term.

%t With[{nn = 54}, Take[#, nn] &@ Union@ Flatten@ Table[Function[p, Map[Times @@ # &@ # &, #] &@ Select[Map[{p, #} &, Prime@ Range[PrimePi@ p - 1]], PrimeQ[Total@ # + 1] &]]@ Prime@ n, {n, nn + 4}]] (* _Michael De Vlieger_, Aug 01 2017 *)

%t With[{nn=60},Take[Times@@@Select[Subsets[Prime[Range[nn]],{2}],PrimeQ[ Total[ #]+ 1]&]//Union,nn]] (* _Harvey P. Dale_, Aug 02 2017 *)

%o (Python)

%o from sympy import factorint, isprime

%o A290435_list = [n for n in range(2,10**5) if sum(factorint(n).values()) == len(factorint(n)) == 2 and isprime(1+sum(factorint(n).keys()))]

%o (PARI) isok(n) = (bigomega(n)==2) && (omega(n)==2) && isprime(1+vecsum(factor(n)[,1])); \\ _Michel Marcus_, Aug 02 2017

%Y Cf. A001358, A005117, A006881, A286842, A290434.

%K nonn

%O 1,1

%A _Chai Wah Wu_, Aug 01 2017

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Last modified May 31 13:01 EDT 2020. Contains 334748 sequences. (Running on oeis4.)