A110786 To obtain a(n), take the n-th palindrome P = A002113(n) and concatenate it with the smallest palindrome Q such that PQ is a prime.

11, 23, 31, 41, 53, 61, 71, 83, 97, 113, 223, 331, 443, 557, 661, 773, 881, 991, 1013, 1117, 1213, 1319, 14177, 1511, 1613, 171131, 1811, 1913, 2027, 2129, 2221, 232171, 2423, 2521, 2621, 2729, 28211, 2927, 3037, 3137, 32377, 3331, 3433, 3533

Offset: 1

Author

Amarnath Murthy, Aug 12 2005

Keywords

• base
• easy
• nonn

Examples

			The palindrome 171 gives a prime 171131 when concatenated with 131 and no palindrome less than 131 gives a prime on concatenation: 1711,1713,1717,1719,17111, etc. up to 171121 are all composite.
		

Crossrefs

Cf. A030675, A110787.

Programs

Python

from itertools import count
from sympy import isprime
def A110786(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(pq:=int(s+str((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 pq # Chai Wah Wu, Jul 10 2024

Extensions

More terms from Giovanni Resta, Feb 08 2006

Edited by N. J. A. Sloane, Jan 16 2009