A125664 Numbers such that the right half of the digits form a prime and the left half do not.

12, 13, 15, 17, 42, 43, 45, 47, 62, 63, 65, 67, 82, 83, 85, 87, 92, 93, 95, 97, 102, 103, 105, 107, 112, 113, 115, 117, 122, 123, 125, 127, 132, 133, 135, 137, 142, 143, 145, 147, 152, 153, 155, 157, 162, 163, 165, 167, 172, 173, 175, 177, 182, 183, 185, 187

Offset

1,1

Comments

If the number of digits in the number is odd > 1, then the middle digit is ignored.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Formula

The left half of an n-digit number is the first floor(n/2) digits. The right half of an n-digit number is the last floor(n/2) digits.

Example

12 is the first number with this property.

Prog

(PARI) rightprime(n) = { local(x, ln, y, lp, rp); for(x=1, n, y=Str(x); if(x > 9, ln=floor(length(y)/2), ln=1); lp = eval(left(y, ln)); rp = eval(right(y, ln)); if(!isprime(lp)&& isprime(rp), print1(x", ") ) ) }
(Python)
from sympy import isprime
def ok(n):
    if n < 10: return False
    s = str(n)
    m = len(s)//2
    return isprime(int(s[-m:])) and not isprime(int(s[:m]))
print([k for k in range(188) if ok(k)]) # Michael S. Branicky, Dec 13 2021

Crossrefs

Cf. A125524.

Sequence in context: A127354 A226099 A179512 * A262210 A074164 A076085

Adjacent sequences: A125661 A125662 A125663 * A125665 A125666 A125667

Keyword

base,easy,nonn

Author

Cino Hilliard, Jan 29 2007

Status

approved