%I #13 Aug 28 2021 02:52:40
%S 2,3,5,7,11,131,171,191,232,292,313,373,414,434,474,535,595,616,676,
%T 717,737,797,838,898,979,101,10301,10701,10901,11311,12721,131,13731,
%U 13931,14941,151,15751,16361,16761,17371,17971,181,191,19391,19791,1991,2112,22322
%N Smallest palindrome beginning with n-th prime.
%C 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.
%H T. D. Noe, <a href="/A185267/b185267.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A082216(A000040(n)).
%e a(6) = 131 because that is the smallest palindrome beginning (base 10) with p(6) = 13.
%o (Python)
%o from sympy import prime
%o def A185267(n):
%o p = prime(n)
%o s = str(p)
%o if s == s[::-1]:
%o return p
%o for i in range(1,len(s)):
%o if s[i:] == s[-1:i-1:-1]:
%o return int(s+s[i-1::-1]) # _Chai Wah Wu_, Aug 27 2021
%Y Cf. A000040, A002385, A082216.
%K nonn,base,easy
%O 1,1
%A _Jonathan Vos Post_, Feb 19 2011