A243374 Least number k such that n//k and k//n are both prime where // is the concatenation function, or 0 if no such k exists.

1, 0, 1, 0, 0, 0, 1, 0, 7, 0, 3, 0, 1, 0, 0, 0, 3, 0, 7, 0, 13, 0, 11, 0, 0, 0, 1, 0, 27, 0, 1, 0, 7, 0, 0, 0, 3, 0, 7, 0, 9, 0, 39, 0, 0, 0, 9, 0, 1, 0, 19, 0, 51, 0, 0, 0, 1, 0, 3, 0, 7, 0, 1, 0, 0, 0, 3, 0, 49, 0, 9, 0, 3, 0, 0, 0, 17, 0, 19, 0, 1, 0, 9, 0, 0, 0, 7, 0, 23

Offset: 1

Author

Derek Orr, Jun 06 2014

Keywords

• nonn
• base

Comments

If n ends in a 2, 4, 5, 6, 8, or 0, then a(n) = 0. It is conjectured that the converse is true.

If a(n) = 1, then n is in A068673.

a(n) is odd or 0 for all n.

Examples

			91 and 19 are not both prime, 92 and 29 are not both prime, 93 and 39 are not both prime, 94 and 49 are not both prime, 95 and 59 are not both prime, 96 and 69 are not both prime, but 97 and 79 are both prime. Thus a(9) = 7.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000 (first 88 terms from Derek Orr)

Crossrefs

Cf. A068673.

Programs

PARI

a(n)=for(k=1,10^4,if(ispseudoprime(eval(concat(Str(n),Str(k)))) && ispseudoprime(eval(concat(Str(k),Str(n)))),return(k)))
n=1;while(n<100,print1(a(n),", ");n++)

Python

import sympy
from sympy import isprime
def a(n):
  for k in range(1,10**5):
    if isprime(int(str(k)+str(n))) and isprime(int(str(n)+str(k))):
      return k
n = 1
while n < 100:
  print(a(n),end=', ')
  n += 1

Extensions

Inserted a(38)=0 by Paolo P. Lava, Jun 16 2014