A053343 Semiprimes of the form pq where p < q and p + q - 1 is prime.

15, 33, 35, 51, 65, 77, 87, 91, 95, 119, 123, 143, 161, 177, 185, 209, 213, 215, 217, 221, 247, 259, 287, 303, 321, 329, 335, 341, 371, 377, 395, 403, 407, 411, 427, 437, 447, 469, 473, 485, 511, 515, 527, 533, 537, 545, 551, 573, 581, 591, 611, 629, 635

Offset: 1

Author

Labos Elemer, Jan 05 2000

Keywords

• nonn
• easy

Comments

Squarefree terms of A050530 with 2 prime divisors.

All terms are odd. - Muniru A Asiru, Aug 29 2017

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Hacène Belbachir, Oussama Igueroufa, Combinatorial interpretation of bisnomial coefficients and Generalized Catalan numbers, Proceedings of the 1st International Conference on Algebras, Graphs and Ordered Sets (ALGOS 2020), hal-02918958 [math.cs], 47-54.

Crossrefs

Subsequence of A291318.

Cf. A050530, A290434, A290435.

Programs

GAP

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

Mathematica

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

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

Formula

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

Extensions

New name from Vincenzo Librandi Aug 23 2017