A350420 - OEIS

%I #10 Dec 30 2021 17:28:14

%S 11,29,41,47,53,59,73,101,107,131,139,151,173,181,197,199,211,257,271,

%T 311,317,331,373,389,401,461,467,479,491,509,521,523,541,563,593,599,

%U 601,607,619,647,677,719,727,743,751,809,827,919,929,947,971,977,1013,1019,1021,1033,1049,1061,1063

%N Primes p such that p*q+q-p is a semiprime, where q is the next prime after p.

%H Robert Israel, <a href="/A350420/b350420.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 41 is a term because it is prime, the next prime is 43, and 41*43 + 43 - 41 = 1765 = 5*363 is a semiprime.

%p q:= 2: R:= NULL: count:= 0:

%p while count < 100 do

%p p:= q; q:= nextprime(q);

%p s:= p*q+q-p;

%p if numtheory:-bigomega(s)=2 then

%p   count:= count+1; R:= R,p;

%p fi

%p od:

%p R;

%Y Cf. A001358, A138170.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Dec 30 2021