A210515 - OEIS

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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

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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: