A210511 Primes formed by concatenating k, k, and 1 for k >= 1.

331, 661, 881, 991, 18181, 20201, 21211, 26261, 27271, 32321, 33331, 41411, 48481, 51511, 54541, 57571, 60601, 65651, 69691, 71711, 78781, 86861, 89891, 90901, 92921, 98981, 99991, 1041041, 1051051, 1131131, 1191191, 1201201, 1221221, 1231231, 1261261, 1281281

Offset: 1

Author

Abhiram R Devesh, Jan 26 2013

Keywords

• nonn
• easy
• base

Comments

This sequence is similar to A030458 and A052089.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A030458, A052089.

Programs

Magma

[nn1: n in [1..130] | IsPrime(nn1) where nn1 is Seqint([1] cat Intseq(n) cat Intseq(n))]; // Bruno Berselli, Jan 30 2013

Mathematica

Select[Table[FromDigits[Flatten[{IntegerDigits[n], IntegerDigits[n], {1}}]], {n, 100}], PrimeQ] (* Alonso del Arte, Jan 27 2013 *)
With[{nn=200},Select[FromDigits[Flatten[IntegerDigits[#]]]&/@Thread[ {Range[ nn],Range[nn],1}],PrimeQ]] (* Harvey P. Dale, Aug 17 2013 *)

Python

import numpy as np
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)

Python

from sympy import isprime
from itertools import count, islice
def agen(): yield from filter(isprime, (int(str(k)+str(k)+'1') for k in count(1)))
print(list(islice(agen(), 36))) # Michael S. Branicky, Jul 26 2022