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

1,9

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.

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A068673.

Sequence in context: A244979 A118288 A094153 * A309608 A324479 A355184

Adjacent sequences: A243371 A243372 A243373 * A243375 A243376 A243377

Keyword

nonn,base

Author

Derek Orr, Jun 06 2014

Extensions

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

Status

approved