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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.

%I A210515 #31 Apr 29 2025 04:45:50
%S A210515 1235,4061,8255,22775,24665,36500,44501,52343,54434,57644,58109,59567,
%T A210515 59588,65018,69407,71789,78689,94280,98594,106748,114272,122504,
%U A210515 134369,137129,138905,144302,162236,196439,235808,238235,269912,277919,278633,282461,290534
%N 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.
%C A210515 The primes generated are part of the sequences A210511, A210512, A210513 and A210514.
%C A210515 There are no terms N with d = 3, 9, 15, 21, ... decimal digits since in those cases (10^(d+1)+10) is divisible by 7. - _Michael S. Branicky_, Apr 28 2025
%H A210515 Michael S. Branicky, <a href="/A210515/b210515.txt">Table of n, a(n) for n = 1..10000</a>
%t A210515 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 *)
%o A210515 (Python)
%o A210515 import numpy as np
%o A210515 from functools import reduce
%o A210515 def factors(n):
%o A210515     return reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))
%o A210515 for i in range(1,50000):
%o A210515     p1=int(str(i)+str(i)+"1")
%o A210515     p3=int(str(i)+str(i)+"3")
%o A210515     p7=int(str(i)+str(i)+"7")
%o A210515     p9=int(str(i)+str(i)+"9")
%o A210515     if len(factors(p1))<3 and len(factors(p3))<3 and len(factors(p7))<3 and len(factors(p9))<3:
%o A210515         print(i, end=',')
%o A210515 (Python)
%o A210515 from gmpy2 import is_prime
%o A210515 def ok(n):
%o A210515     b = n*(10**len(str(n))+1)*10
%o A210515     return all(is_prime(b+x) for x in [1, 3, 7, 9])
%o A210515 print([N for N in range(3*10**5) if ok(N)]) # _Michael S. Branicky_, Apr 28 2025
%Y A210515 Cf. A210511, A210512, A210513, A210514.
%K A210515 nonn,base
%O A210515 1,1
%A A210515 _Abhiram R Devesh_, Jan 26 2013