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A210512 Primes formed by concatenating n, n and 3 for n >= 1. 2
113, 223, 443, 773, 883, 10103, 11113, 14143, 25253, 26263, 28283, 32323, 35353, 41413, 50503, 61613, 68683, 71713, 77773, 80803, 83833, 85853, 88883, 97973, 1001003, 1011013, 1101103, 1131133, 1161163, 1181183, 1221223, 1241243, 1281283, 1331333, 1361363, 1391393 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This series is similar to A030458, A052089 and A210511.

n must not be a multiple of 3, otherwise the concatenation of n, n, 3 will also be a multiple of 3 and therefore not prime. This is a necessary but not sufficient condition.

LINKS

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

MATHEMATICA

Select[Table[FromDigits[Flatten[{IntegerDigits[n], IntegerDigits[n], {3}}]], {n, 100}], PrimeQ] (* Alonso del Arte, Jan 27 2013 *)

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, 1000):

    p1=int(str(i)+str(i)+"3")

    if len(factors(p1))<3:

        print(p1, end=', ')

(Python)

from sympy import isprime

def xf(n): return int(str(n)*2+'3')

def ok(n): return isprime(xf(n))

print(list(map(xf, filter(ok, range(1, 140))))) # Michael S. Branicky, May 21 2021

(MAGMA) [nn3: n in [1..140] | IsPrime(nn3) where nn3 is Seqint([3] cat Intseq(n) cat Intseq(n))]; // Bruno Berselli, Jan 30 2013

CROSSREFS

Cf. A030458, A052089, A210511.

Sequence in context: A054696 A142426 A309617 * A319936 A142700 A142002

Adjacent sequences:  A210509 A210510 A210511 * A210513 A210514 A210515

KEYWORD

base,nonn,easy

AUTHOR

Abhiram R Devesh, Jan 26 2013

STATUS

approved

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Last modified September 28 10:48 EDT 2021. Contains 347714 sequences. (Running on oeis4.)