A249666 -id:A249666

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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.

+10
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.

KEYWORD

nonn

AUTHOR

Antonio Roldán, Dec 03 2014

STATUS

approved

A249624

Numbers n such that the sum of n and the least prime>n (A151800(n)) is prime.

+10
3

0, 1, 2, 6, 8, 14, 18, 20, 24, 30, 34, 36, 38, 48, 50, 54, 64, 68, 78, 80, 84, 94, 96, 98, 104, 110, 114, 124, 132, 134, 138, 144, 154, 156, 164, 174, 182, 188, 198, 208, 210, 216, 220, 228, 230, 248, 252, 258, 260, 270, 284, 294, 300, 306, 308, 314, 322, 328, 330, 336, 344, 360

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..62.

EXAMPLE

50 is in the sequence because A151800(50)=53, and 50+53=103 is prime.

PROG

(PARI){for(i=0, 10^3, k=i+nextprime(i+1); if(isprime(k), print1(i, ", ")))}

CROSSREFS

Cf. A151800, A249666, A249667, A249676.

KEYWORD

nonn

AUTHOR

Antonio Roldán, Dec 03 2014

STATUS

approved

A249676

Terms k of A249667 such that k-A151799(k) = A151800(k)-k.

+10
3

6, 30, 50, 144, 300, 560, 610, 650, 660, 714, 780, 810, 816, 870, 1120, 1176, 1190, 1806, 2130, 2470, 2490, 2550, 2922, 3030, 3240, 3330, 3390, 3480, 3600, 3620, 3840, 4266, 4368, 5796, 5850, 6270, 6786, 6954, 7074, 7710, 8280, 9400, 9990, 10146, 10350, 10380, 10530, 10660, 11064

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..49.

EXAMPLE

610 is in A249667: the least prime>610 is 613, and 610+613=1223 is prime; the largest prime<610 is 607, and 610+607=1217 is prime. Also, 613-610=610-607=3, then 610 is in the current sequence.

PROG

(PARI) {for(i=3, 2*10^4, m=nextprime(i+1); k=i+m; n=precprime(i-1); q=i+n; if(isprime(k)&&isprime(q)&&m-i==i-n, print1(i, ", ")))}

CROSSREFS

Cf. A249624, A249666, A249667.

KEYWORD

nonn

AUTHOR

Antonio Roldán, Dec 03 2014

STATUS

approved

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