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Smallest prime of the form "Concatenate(m,n,m)".
1

%I #41 Mar 16 2020 16:48:59

%S 101,313,727,131,11411,151,13613,373,181,191,9109,131113,7127,171317,

%T 131413,1151,3163,1171,1181,9199,1201,112111,172217,1231,7247,3253,

%U 372637,172717,232823,1291,1301,3313,1321,233323,3343,273527,1361,3373,1381,173917,174017

%N Smallest prime of the form "Concatenate(m,n,m)".

%H Danny Rorabaugh, <a href="/A252942/b252942.txt">Table of n, a(n) for n = 0..10000</a>

%e 111 is divisible by 3, and 212 is divisible by 2, but 313 is prime; therefore, a(1) = 313.

%p f:= proc(n) local dn, x, dx,p;

%p dn:= 10^(1+ilog10(n));

%p for x from 1 by 2 do if igcd(x,n) = 1 then

%p dx:= 10^(1+ilog10(x));

%p p:= x*(1+dx*dn)+n*dx;

%p if isprime(p) then return(p) fi

%p fi od

%p end proc:

%p 101, seq(f(n), n=1..100); # _Robert Israel_, Apr 07 2015

%p # second Maple program:

%p a:= proc(n) local m, p; for m do

%p p:= parse(cat(m, n, m));

%p if isprime(p) then break fi od; p

%p end:

%p seq(a(n), n=0..50); # _Alois P. Heinz_, Mar 16 2020

%t mnmPrimes = {}; f[m_, n_] := FromDigits[Flatten[{IntegerDigits[m], IntegerDigits[n], IntegerDigits[m]}]]; Do[m = 1; While[True, If[PrimeQ[f[m, n]], AppendTo[mnmPrimes, f[m, n]]; Break[]]; m+=2], {n, 0, 40}]; mnmPrimes

%o (PARI) a(n) = {m=1; while (! isprime(p=eval(concat(Str(m), concat(Str(n), Str(m))))), m+=2); p;} \\ _Michel Marcus_, Mar 23 2015

%o (Sage)

%o def A252942(n):

%o m = 1

%o sn = str(n)

%o while True:

%o sm = str(m)

%o a = int(sm + sn + sm)

%o if is_prime(a):

%o return a

%o m += 2

%o A252942(40) # _Danny Rorabaugh_, Mar 31 2015

%o (Haskell)

%o a252942 n = head [y | m <- [1..],

%o let y = read (show m ++ show n ++ show m) :: Integer, a010051' y == 1]

%o -- _Reinhard Zumkeller_, Apr 08 2015

%Y Cf. A090287, A256048.

%Y Cf. A010051.

%K base,easy,nonn

%O 0,1

%A _Ivan N. Ianakiev_, Mar 23 2015