A343448 - OEIS

%I #11 Apr 15 2021 23:41:49

%S 5,7,11,13,19,29,37,67,71,101,103,107,193,223,229,281,293,337,359,367,

%T 541,569,613,631,647,677,709,751,809,823,829,857,881,887,919,947,971,

%U 1009,1019,1049,1237,1249,1279,1373,1439,1471,1543,1571,1627,1637,1693,1733,1783,1907,1993,2017,2161

%N Primes p such that p+q*(r+s) is prime, where p,q,r,s are consecutive primes.

%C Includes p if p, q = p+2, r = p+6, s = p+8 are consecutive primes and 2*p^2+19*p+28 is prime. The generalized Dickson's conjecture implies there are infinitely many such p.

%H Robert Israel, <a href="/A343448/b343448.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 11 is a term because 11,13,17 and 19 are consecutive primes and 11+13*(17+19) = 479 is prime.

%p A:= NULL: q:= 2: r:= 3: s:= 5: count:= 0:

%p while count < 100 do

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

%p   v:= p+q*(r+s);

%p   if isprime(v) then A:= A,p; count:= count+1 fi

%p od:

%p A;

%o (Python)

%o from sympy import isprime, nextprime

%o def aupto(limit):

%o   p, q, r, s, alst = 2, 3, 5, 7, []

%o   while p <= limit:

%o     if isprime(p + q*(r+s)): alst.append(p)

%o     p, q, r, s = q, r, s, nextprime(s)

%o   return alst

%o print(aupto(2161)) # _Michael S. Branicky_, Apr 15 2021

%Y Cf. A343449.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Apr 15 2021