%I #25 Mar 09 2016 16:37:57

%S 6,24,30,36,50,54,78,84,114,132,144,156,174,210,220,252,294,300,306,

%T 330,360,378,474,492,510,512,528,546,560,594,610,650,660,690,714,720,

%U 762,780,800,804,810,816,870,912,996,1002,1068,1074,1104,1120,1170,1176,1190,1210,1236,1262

%N Numbers n such that the sum of n and the largest prime<n is prime, and the sum of n and the least prime>n is also prime.

%C This sequence is the intersection of A249624 and A249666.

%H Chai Wah Wu, <a href="/A249667/b249667.txt">Table of n, a(n) for n = 1..3410</a>

%e 114 is in the sequence because the least prime>114 is 127 and 114+127=241 is prime; the largest prime<114 is 113 and 114+113=227 is prime. Also, 114 is in A249624 and A249666.

%t Select[Range[1500],AllTrue[#+{NextPrime[#],NextPrime[#,-1]},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Mar 09 2016 *)

%o (PARI) {for(i=3,2*10^3,k=i+nextprime(i+1);q=i+precprime(i-1);if(isprime(k)&&isprime(q),print1(i,", ")))}

%o (Python)

%o from gmpy2 import is_prime, next_prime

%o A249667_list, p = [], 2

%o for _ in range(10**4):

%o ....q = next_prime(p)

%o ....n1 = 2*p+1

%o ....n2 = p+q+1

%o ....while n1 < p+q:

%o ........if is_prime(n1) and is_prime(n2):

%o ............A249667_list.append(n1-p)

%o ........n1 += 2

%o ........n2 += 2

%o ....p = q # _Chai Wah Wu_, Dec 06 2014

%Y Cf. A249624, A249666, A249676.

%K nonn

%O 1,1

%A _Antonio Roldán_, Dec 03 2014