A210514 Prime numbers generated by concatenating k, k, and 9.

229, 449, 11119, 14149, 22229, 28289, 31319, 37379, 44449, 49499, 52529, 56569, 67679, 70709, 71719, 80809, 86869, 89899, 94949, 95959, 1061069, 1101109, 1131139, 1151159, 1161169, 1191199, 1241249, 1251259, 1331339, 1401409, 1431439, 1481489, 1571579, 1601609

Offset: 1

Author

Abhiram R Devesh, Jan 26 2013

Keywords

• base
• nonn
• easy

Comments

This series is similar to A030458 and A052089.

Base considered is 10.

Examples

			For k=2, a(1)= 229.
For k=4, a(2)= 449.
For k=11, a(3)= 11119.
For k=14, a(4)= 14149.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A030458, A052089.

Programs

Mathematica

Select[Table[FromDigits[Flatten[Join[IntegerDigits/@{n,n},{9}]]],{n,200}],PrimeQ] (* Harvey P. Dale, Apr 23 2015 *)

Python

import numpy as np
from functools import reduce
def factors(n):
    return reduce(list._add_, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))
for i in range(1, 2000):
    p1=int(str(i)+str(i)+"1")
    if len(factors(p1))<3:
        print(p1, end=',')

Python

from sympy import isprime
from itertools import count, islice
def agen(): yield from filter(isprime, (int(str(k)+str(k)+'9') for k in count(1)))
print(list(islice(agen(), 34))) # Michael S. Branicky, Jul 26 2022

Extensions

a(27) and beyond from Michael S. Branicky, Jul 26 2022