A252942 Smallest prime of the form "Concatenate(m,n,m)".
101, 313, 727, 131, 11411, 151, 13613, 373, 181, 191, 9109, 131113, 7127, 171317, 131413, 1151, 3163, 1171, 1181, 9199, 1201, 112111, 172217, 1231, 7247, 3253, 372637, 172717, 232823, 1291, 1301, 3313, 1321, 233323, 3343, 273527, 1361, 3373, 1381, 173917, 174017
Offset: 0
Examples
111 is divisible by 3, and 212 is divisible by 2, but 313 is prime; therefore, a(1) = 313.
Links
- Danny Rorabaugh, Table of n, a(n) for n = 0..10000
Programs
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Haskell
a252942 n = head [y | m <- [1..], let y = read (show m ++ show n ++ show m) :: Integer, a010051' y == 1] -- Reinhard Zumkeller, Apr 08 2015
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Maple
f:= proc(n) local dn, x, dx,p; dn:= 10^(1+ilog10(n)); for x from 1 by 2 do if igcd(x,n) = 1 then dx:= 10^(1+ilog10(x)); p:= x*(1+dx*dn)+n*dx; if isprime(p) then return(p) fi fi od end proc: 101, seq(f(n), n=1..100); # Robert Israel, Apr 07 2015 # second Maple program: a:= proc(n) local m, p; for m do p:= parse(cat(m, n, m)); if isprime(p) then break fi od; p end: seq(a(n), n=0..50); # Alois P. Heinz, Mar 16 2020 -
Mathematica
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 -
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 -
Sage
def A252942(n): m = 1 sn = str(n) while True: sm = str(m) a = int(sm + sn + sm) if is_prime(a): return a m += 2 A252942(40) # Danny Rorabaugh, Mar 31 2015