A210515 Numbers N such that concatenation of N, N, and x generates a prime for x=1 and x=3 and x=7 and x=9.

1235, 4061, 8255, 22775, 24665, 36500, 44501, 52343, 54434, 57644, 58109, 59567, 59588, 65018, 69407, 71789, 78689, 94280, 98594, 106748, 114272, 122504, 134369, 137129, 138905, 144302, 162236, 196439, 235808, 238235, 269912, 277919, 278633, 282461, 290534

Offset

1,1

Comments

The primes generated are part of the sequences A210511, A210512, A210513 and A210514.

Links

Table of n, a(n) for n=1..35.

Mathematica

Select[Range[3*10^5], AllTrue[FromDigits/@Table[Join[IntegerDigits[#], IntegerDigits [#], {n}], {n, {1, 3, 7, 9}}], PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 07 2021 *)

Prog

(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, 50000):
    p1=int(str(i)+str(i)+"1")
    p3=int(str(i)+str(i)+"3")
    p7=int(str(i)+str(i)+"7")
    p9=int(str(i)+str(i)+"9")
    if len(factors(p1))<3 and len(factors(p3))<3 and len(factors(p7))<3 and len(factors(p9))<3:
        print(i, end=', ')

Crossrefs

Cf. A210511, A210512, A210513, A210514.

Sequence in context: A193492 A279204 A091332 * A122043 A179913 A161868

Adjacent sequences: A210512 A210513 A210514 * A210516 A210517 A210518

Keyword

base,nonn,easy

Author

Abhiram R Devesh, Jan 26 2013

Status

approved