A248620 Lesser of twin primes of (29n + 1, 29n + 3).

59, 1277, 1451, 3539, 4931, 5279, 9281, 9629, 10499, 11717, 12239, 16067, 22157, 23027, 23201, 24419, 26681, 31727, 34511, 35729, 37991, 40427, 45821, 47387, 48779, 55217, 59219, 60089, 70181, 70877, 72269, 75401, 77489, 79229, 80447, 83231, 85667, 88799

Offset: 1

Author

Karl V. Keller, Jr., Oct 10 2014

Keywords

• nonn

Comments

Lesser of twin primes where A195819(n) + 1 and A195819(n) + 3 are both primes.

Intersection of A001359 and A141977.

Examples

			29 * 2 + 1 = 59, which is prime, and 61 is also prime, so 59 is in the sequence.
29 * 44 + 1 = 1277, which is prime, and 1279 is also prime, so 1277 is in the sequence.
29 * 50 + 1 = 1451, which is prime, and 1453 is also prime, so 1451 is in the sequence.
29 * 54 + 1 = 1567, which is prime, but 1569 = 3 * 523, so 1567 is not in the sequence.
		

Links

• Karl V. Keller, Jr., Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001359 (Lesser of twin primes), A195819 (Multiples of 29).

Cf. A141977 (Primes congruent to 1 mod 29), A141979 (Primes congruent to 3 mod 29).

Programs

Mathematica

Select[58Range[1500] + 1, PrimeQ[#] && PrimeQ[# + 2] &] (* Alonso del Arte, Oct 31 2014 *)
Select[29*Range[2,3150,2],AllTrue[#+{1,3},PrimeQ]&]+1 (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 16 2019 *)

PARI

lista(nn) = {forstep (n=2, nn, 2, if (isprime(p=29*n+1) && isprime(29*n+3), print1(p, ", ")););} \\ Michel Marcus, Oct 17 2014

Python

from math import *
from sympy import isprime
for n in range(0,10001):
  if isprime(58*n+1) and isprime(58*n+3): print (58*n+1,end=', ')