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Palindromic prime numbers == 2 (mod 9).
1

%I #15 Jun 02 2024 15:19:05

%S 2,11,101,191,353,929,13331,16661,17471,19991,36263,38783,70607,72227,

%T 73037,74747,75557,76367,78887,79697,91019,94349,1074701,1082801,

%U 1123211,1180811,1221221,1262621,1287821,1303031,1311131,1328231,1360631,1508051,1532351

%N Palindromic prime numbers == 2 (mod 9).

%H Shyam Sunder Gupta, <a href="/A229876/b229876.txt">Table of n, a(n) for n = 1..994</a>

%t t = {}; Do[z = n*10^(IntegerLength[n] - 1) + FromDigits@Rest@Reverse@IntegerDigits[n]; If[PrimeQ[z] && Mod[z, 9] == 2, AppendTo[t, z]], {n, 1, 99999}]; Insert[t, 11, 2]

%t Select[Prime[Range[120000]],PalindromeQ[#]&&Mod[#,9]==2&] (* _Harvey P. Dale_, Jun 02 2024 *)

%Y Cf. A002385, A229875.

%K nonn,base,less

%O 1,1

%A _Shyam Sunder Gupta_, Oct 02 2013