A245727 Least number k >= 0 such that n concatenated with n + k is prime.

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, 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, 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

Offset: 1

Author

Derek Orr, Jul 30 2014

Keywords

• nonn
• base

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A228325.

Programs

Maple

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:
seq(a(n),n=1..100); # Robert Israel, Jul 30 2014

Mathematica

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 *)

PARI

a(n) = for(k=n,10^4,if(isprime(eval(concat(Str(n),Str(k)))),return(k-n)))
vector(150,n,a(n))

Python

def a(n):
  for k in range(n,10**4):
    if isprime(str(n)+str(k)):
      return k-n
n = 1
while n < 150:
  print(a(n),end=', ')
  n += 1

Formula

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