A185267 Smallest palindrome beginning with n-th prime.

2, 3, 5, 7, 11, 131, 171, 191, 232, 292, 313, 373, 414, 434, 474, 535, 595, 616, 676, 717, 737, 797, 838, 898, 979, 101, 10301, 10701, 10901, 11311, 12721, 131, 13731, 13931, 14941, 151, 15751, 16361, 16761, 17371, 17971, 181, 191, 19391, 19791, 1991, 2112, 22322

Offset: 1

Author

Jonathan Vos Post, Feb 19 2011

Keywords

• nonn
• base
• easy

Comments

a(n) is itself prime for n = 1, 2, 3, 4, 5, 6, 8, 11, 12, 22, 26, 27, 30, 31, 32, 34, ... where a(n) = 2, 3, 5, 7, 11, 131, 191, 313, 373, 797, 101, 10301, 11311, 12721, 131, 13931, which are also in A002385. Although 979 begins with the prime p(25) = 97, and is a palindrome, it is not in the commented subsequence because 979 = 11 * 89 is semiprime rather than prime.

Examples

			a(6) = 131 because that is the smallest palindrome beginning (base 10) with p(6) = 13.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A002385, A082216.

Programs

Python

from sympy import prime
def A185267(n):
    p = prime(n)
    s = str(p)
    if s == s[::-1]:
        return p
    for i in range(1,len(s)):
        if s[i:] == s[-1:i-1:-1]:
            return int(s+s[i-1::-1]) # Chai Wah Wu, Aug 27 2021

Formula

a(n) = A082216(A000040(n)).