A341934 - OEIS

%I #12 Feb 25 2021 13:25:13

%S 2,3,5,7,11,13,17,19,23,29,73,101,107,109,137,191,199,251,257,293,317,

%T 349,353,421,461,571,647,659,683,773,787,811,827,853,859,877,883,887,

%U 919,929,941,997,1031,1087,1319,1429,1453,1471,1481,1483,1543,1567,1627,1697,1699,1721,1723,1753,1789

%N Primes p such that 2*p*q-2*q*r+r*s is prime, where p,q,r,s are consecutive primes.

%C Includes the first 10 primes.

%C If p is prime, the next four primes are p+2, p+6, p+12 and p+14, and p^2+6*p+48 is prime, then the twin primes p and p+2 are in the sequence, with the same value of A341937.

%H Robert Israel, <a href="/A341934/b341934.txt">Table of n, a(n) for n = 1..10000</a>

%e a(5) = 11 is a term because (p,q,r,s)=(11,13,17,19) are consecutive primes with 2*p*q-2*q*r+r*s = 167, which is prime.

%p P:= select(isprime, [2,seq(i,i=3..10000,2)]):

%p B:= select(i -> isprime(P[i+2]*P[i+3]-2*P[i+1]*(P[i+2]-P[i])), [$1..nops(P)-3]):

%p P[B];

%o (Python)

%o from sympy import isprime, nextprime

%o p,q,r,s,A341934_list=2,3,5,7,[]

%o while p < 10**6:

%o     if isprime(2*q*(p-r)+r*s):

%o         A341934_list.append(p)

%o     p, q, r, s = q, r, s, nextprime(s) # _Chai Wah Wu_, Feb 24 2021

%Y Cf. A341937.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Feb 23 2021