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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A294900 A064510 A228383 * A114274 A292985 A234648

Adjacent sequences:  A249664 A249665 A249666 * A249668 A249669 A249670

KEYWORD

nonn

AUTHOR

Antonio Roldán, Dec 03 2014

STATUS

approved

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Last modified September 21 19:29 EDT 2018. Contains 315260 sequences. (Running on oeis4.)