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Smallest palindrome beginning with n-th prime.
1

%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