A110787 Least palindrome which when appended to the n-th palindrome gives a prime.

1, 3, 1, 1, 3, 1, 1, 3, 7, 3, 3, 1, 3, 7, 1, 3, 1, 1, 3, 7, 3, 9, 77, 1, 3, 131, 1, 3, 7, 9, 1, 171, 3, 1, 1, 9, 11, 7, 7, 7, 77, 1, 3, 3, 1, 3, 3, 1, 9, 11, 1, 9, 1, 7, 3, 101, 111, 3, 1, 3, 11, 1, 77, 7, 1, 131, 1, 3, 7, 3, 3, 1, 9, 3, 1, 1, 3, 1, 9, 7, 33, 111, 7, 3, 3, 11, 3, 77, 1, 99, 7, 7, 11, 1, 1

Offset: 1

Author

Amarnath Murthy, Aug 12 2005

Keywords

• base
• easy
• nonn

Comments

A002113(n) concatenated with a(n) is a prime. A110786(n) is that prime. - Franklin T. Adams-Watters, Oct 11 2006

Crossrefs

Cf. A110786.

Programs

Python

from itertools import count
from sympy import isprime
def A110787(n):
    s = str((c:=n+1-x)*x+int(str(c)[-2::-1] or 0) if n+1<(x:=10**(len(str(n+1>>1))-1))+(y:=10*x) else (c:=n+1-y)*y+int(str(c)[::-1] or 0))
    for k in count(2):
        if isprime(int(s+str(q:=(c:=k-x)*x+int(str(c)[-2::-1] or 0) if k<(x:=10**(len(str(k>>1))-1))+(y:=10*x) else (c:=k-y)*y+int(str(c)[::-1] or 0)))):
            return int(q) # Chai Wah Wu, Jul 10 2024

Extensions

More terms from Franklin T. Adams-Watters, Oct 11 2006