A053343 - OEIS

%I #18 Nov 03 2020 01:40:02

%S 15,33,35,51,65,77,87,91,95,119,123,143,161,177,185,209,213,215,217,

%T 221,247,259,287,303,321,329,335,341,371,377,395,403,407,411,427,437,

%U 447,469,473,485,511,515,527,533,537,545,551,573,581,591,611,629,635

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

%C Squarefree terms of A050530 with 2 prime divisors.

%C All terms are odd. - _Muniru A Asiru_, Aug 29 2017

%H Vincenzo Librandi, <a href="/A053343/b053343.txt">Table of n, a(n) for n = 1..1000</a>

%H Hacène Belbachir, Oussama Igueroufa, <a href="https://hal.archives-ouvertes.fr/hal-02918958/document#page=48">Combinatorial interpretation of bisnomial coefficients and Generalized Catalan numbers</a>, Proceedings of the 1st International Conference on Algebras, Graphs and Ordered Sets (ALGOS 2020), hal-02918958 [math.cs], 47-54.

%F n=pq such that n-phi(n) = pq-(p-1)(q-1) = p+q-1 is prime.

%t With[{nn=70}, Take[Times@@@Select[Subsets[Prime[Range[nn]], {2}], PrimeQ[Total[#] - 1] &]//Union, nn]] (* _Vincenzo Librandi_, Aug 23 2017 *)

%o (PARI) list(lim)=my(v=List()); forprime(p=5,lim\3, forprime(q=3,min(lim\p,p-2), if(isprime(p+q-1), listput(v,p*q)))); Set(v) \\ _Charles R Greathouse IV_, Aug 23 2017

%o (GAP)

%o A053343:=List(Filtered(Filtered(List(Filtered(List([1..10^5],Factors),i->Length(i)=2),Set),j->Length(j)=2),i->IsPrime(Sum(i)-1)),Product); # _Muniru A Asiru_, Aug 29 2017

%Y Subsequence of A291318.

%Y Cf. A050530, A290434, A290435.

%K nonn,easy

%O 1,1

%A _Labos Elemer_, Jan 05 2000

%E New name from _Vincenzo Librandi_ Aug 23 2017