A245727 - OEIS

%I #16 Oct 05 2014 10:37:39

%S 0,1,4,3,4,1,2,1,2,3,6,1,6,9,8,3,4,5,12,7,8,15,10,13,6,7,2,5,10,7,6,

%T 19,10,15,4,1,2,9,4,9,12,1,6,3,2,3,4,13,2,1,2,9,28,17,2,1,22,3,22,7,2,

%U 1,4,5,4,7,12,1,2,9,6,11,20,3,2,5,12,1,14,1,10,5,4,37,12,3,16,5,10

%N Least number k >= 0 such that n concatenated with n + k is prime.

%H Alois P. Heinz, <a href="/A245727/b245727.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A228325(n) - n for n > 1.

%e 33 is not prime. 34 is not prime. 35 is not prime. 36 is not prime. 37 is prime. Since 7 is 4 more than 3, a(3) = 4.

%p a:= proc(n) local j; for j from n do if isprime(n*10^(1+ilog10(j))+j) then return(j-n) fi od end proc:

%p seq(a(n),n=1..100); # _Robert Israel_, Jul 30 2014

%t lnk[n_]:=Module[{k=0,idn=IntegerDigits[n]},While[!PrimeQ[FromDigits[ Join[ idn, IntegerDigits[ n+k]]]],k++];k]; Array[lnk,90] (* _Harvey P. Dale_, Oct 05 2014 *)

%o (PARI)

%o a(n) = for(k=n,10^4,if(isprime(eval(concat(Str(n),Str(k)))),return(k-n)))

%o vector(150,n,a(n))

%o (Python)

%o def a(n):

%o ..for k in range(n,10**4):

%o ....if isprime(str(n)+str(k)):

%o ......return k-n

%o n = 1

%o while n < 150:

%o ..print(a(n),end=', ')

%o ..n += 1

%Y Cf. A228325.

%K nonn,base

%O 1,3

%A _Derek Orr_, Jul 30 2014