A249667 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.

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

1,1

Comments

This sequence is the intersection of A249624 and A249666.

Links

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

Example

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.

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 *)

Prog

(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(n1-p)
........n1 += 2
........n2 += 2
....p = q # Chai Wah Wu, Dec 06 2014

Crossrefs

Cf. A249624, A249666, A249676.

Sequence in context: A064510 A335736 A228383 * A114274 A335215 A292985

Adjacent sequences: A249664 A249665 A249666 * A249668 A249669 A249670

Keyword

nonn

Author

Antonio Roldán, Dec 03 2014

Status

approved