A249667 Numbers n such that the sum of n and the largest primen is also prime.

6, 24, 30, 36, 50, 54, 78, 84, 114, 132, 144, 156, 174, 210, 220, 252, 294, 300, 306, 330, 360, 378, 474, 492, 510, 512, 528, 546, 560, 594, 610, 650, 660, 690, 714, 720, 762, 780, 800, 804, 810, 816, 870, 912, 996, 1002, 1068, 1074, 1104, 1120, 1170, 1176, 1190, 1210, 1236, 1262

Offset: 1

Author

Antonio Roldán, Dec 03 2014

Keywords

• nonn

Comments

This sequence is the intersection of A249624 and A249666.

Examples

			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.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..3410

Crossrefs

Cf. A249624, A249666, A249676.

Programs

Mathematica

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

PARI

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

Python

from gmpy2 import is_prime, next_prime
A249667_list, p = [], 2
for _ in range(10**4):
    q = next_prime(p)
    n1 = 2*p+1
    n2 = p+q+1
    while n1 < p+q:
        if is_prime(n1) and is_prime(n2):
            A249667_list.append(int(n1-p))
        n1 += 2
        n2 += 2
    p = q # Chai Wah Wu, Dec 06 2014