A249624 -id:A249624 - cp's OEIS frontend

A249666 Numbers n such that the sum of n and the largest primeA151799(n)) is prime.

3, 4, 6, 10, 12, 16, 22, 24, 30, 36, 42, 46, 50, 54, 56, 66, 70, 76, 78, 84, 90, 92, 100, 114, 116, 120, 126, 130, 132, 142, 144, 156, 160, 170, 174, 176, 180, 186, 192, 196, 202, 210, 220, 222, 226, 232, 234, 240, 246, 250, 252, 276, 280, 282, 286, 288, 294, 300, 306, 310, 324

Offset: 1

Antonio Roldán, Dec 03 2014

nonn

			66 is in the sequence because A151799(66)=61, and 66+61=127 is prime.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A151799, A249624, A249667, A249676.

Select[Range[400],PrimeQ[#+NextPrime[#,-1]]&] (* Harvey P. Dale, Aug 04 2019 *)

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

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

Original entry on oeis.org

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

Antonio Roldán, Dec 03 2014

nonn

This sequence is the intersection of A249624 and A249666.

			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.

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

Cf. A249624, A249666, A249676.

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

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

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

A249676 Terms k of A249667 such that k-A151799(k) = A151800(k)-k.

Original entry on oeis.org

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

Offset: 1

Antonio Roldán, Dec 03 2014

nonn

			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.

Cf. A249624, A249666, A249667.

{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,", ")))}

cp's OEIS Frontend

A249666 Numbers n such that the sum of n and the largest primeA151799(n)) is prime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

A249676 Terms k of A249667 such that k-A151799(k) = A151800(k)-k.

Views

Author

Keywords

Examples

Crossrefs

Programs

PARI