%I #10 Feb 12 2021 08:20:20
%S 2,11,101,11113,10301,1011013,1003001,100110013,100030001,10000000019,
%T 10000500001,1000011000017,1000008000001,100000440000011,
%U 100000323000001,10000001100000011,10000000500000001,1000000011000000019,1000000008000000001,100000000660000000013
%N a(n) is the least prime whose representation contains a palindromic substring of length n.
%H Michael S. Branicky, <a href="/A115941/b115941.txt">Table of n, a(n) for n = 1..25</a>
%e a(6)=1011013 since it is the least prime that contains a palindromic substring (101101) of length 6.
%o (Python)
%o from sympy import isprime
%o from itertools import product
%o def pals_to_test(n, odd=True):
%o if n <= 2: yield [2, 11][n-1]
%o if odd: ruled_out = "024568" # can't be even or multiple of 5
%o else: ruled_out = "0"
%o midrange = [[""], [str(i) for i in range(10)]]
%o for p in product("0123456789", repeat=n//2):
%o left = "".join(p)
%o if len(left):
%o if left[0] in ruled_out: continue
%o for middle in midrange[n%2]:
%o out = left+middle+left[::-1]
%o if odd: yield out
%o else:
%o for last in "1379": yield out+last
%o def a(n):
%o palsgen = pals_to_test(n, n%2 == 1)
%o while True:
%o strpal = next(palsgen)
%o pal = int(strpal)
%o if isprime(pal): return pal
%o print([a(n) for n in range(1, 18)]) # _Michael S. Branicky_, Feb 11 2021
%Y Cf. A056732.
%K nonn,base
%O 1,1
%A _Giovanni Resta_, Feb 06 2006
%E a(18) and beyond from _Michael S. Branicky_, Feb 11 2021