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

1,1

Links

Table of n, a(n) for n=1..44.

Example

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.

Prog

(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

Crossrefs

Cf. A030675, A110787.

Sequence in context: A077501 A337845 A030675 * A059642 A090920 A344175

Adjacent sequences: A110783 A110784 A110785 * A110787 A110788 A110789

Keyword

base,easy,nonn

Author

Amarnath Murthy, Aug 12 2005

Extensions

More terms from Giovanni Resta, Feb 08 2006

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

Status

approved