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A210512 Primes formed by concatenating k, k and 3 for k >= 1.

%I A210512 #40 Aug 24 2022 09:39:19
%S A210512 113,223,443,773,883,10103,11113,14143,25253,26263,28283,32323,35353,
%T A210512 41413,50503,61613,68683,71713,77773,80803,83833,85853,88883,97973,
%U A210512 1001003,1011013,1101103,1131133,1161163,1181183,1221223,1241243,1281283,1331333,1361363,1391393
%N A210512 Primes formed by concatenating k, k and 3 for k >= 1.
%C A210512 This sequence is similar to A030458, A052089 and A210511.
%C A210512 k must not be a multiple of 3, otherwise the concatenation of k, k and 3 will also be a multiple of 3 and therefore not prime. This is a necessary but not sufficient condition.
%C A210512 Some of the terms can be found with this simple process: 5 - 3 = 2 = 1 + 1 giving 113; 7 - 3 = 4 = 2 + 2 giving 223; 11 - 3 = 8 = 4 + 4 giving 443; 17 - 3 = 14 = 7 + 7 giving 773; 19 - 3 = 16 = 8 + 8 giving 883. - _J. M. Bergot_, Jul 25 2022
%H A210512 Vincenzo Librandi, <a href="/A210512/b210512.txt">Table of n, a(n) for n = 1..1000</a>
%t A210512 Select[Table[FromDigits[Flatten[{IntegerDigits[n], IntegerDigits[n], {3}}]], {n, 100}], PrimeQ] (* _Alonso del Arte_, Jan 27 2013 *)
%o A210512 (Python)
%o A210512 import numpy as np
%o A210512 from functools import reduce
%o A210512 def factors(n):
%o A210512     return reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) +1) if n % i == 0))
%o A210512 for i in range(1, 1000):
%o A210512     p1=int(str(i)+str(i)+"3")
%o A210512     if len(factors(p1))<3:
%o A210512         print(p1, end=',')
%o A210512 (Python)
%o A210512 from sympy import isprime
%o A210512 def xf(n): return int(str(n)*2+'3')
%o A210512 def ok(n): return isprime(xf(n))
%o A210512 print(list(map(xf, filter(ok, range(1, 140))))) # _Michael S. Branicky_, May 21 2021
%o A210512 (Magma) [nn3: n in [1..140] | IsPrime(nn3) where nn3 is Seqint([3] cat Intseq(n) cat Intseq(n))]; // _Bruno Berselli_, Jan 30 2013
%Y A210512 Cf. A030458, A052089, A210511.
%K A210512 base,nonn,easy
%O A210512 1,1
%A A210512 _Abhiram R Devesh_, Jan 26 2013