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%I #6 Jul 31 2019 10:44:04
%S 3,5,17,31,1201,128199521
%N Tribonacci primes that are also primes when their digits are reversed.
%C This is to A115347 as Fibonacci numbers A000045 are to A000213 tribonacci numbers. Except for palidromatic tribonacci numbers {3, 5, ...} these are tribonacci emirps, A000213 INTERSECTION A006567.
%C The next term, if it exists, is greater than A000213(10000). [From _Dmitry Kamenetsky_, Mar 03 2009]
%F {p such that p is in A000040 and p is in A000213 and R(p) = A004086(p) is in A000040} = {p such that p is in A056816 and R(p) = is in A000040}.
%e a(5) = 1201 because 1201 is prime, and is the 13th tribonacci number A000213(13), and R(1201) = A004086(1201) = 1021 is also prime. a(6) = 128199521 = the 10th tribonacci prime A056816(10), and its digital reverse 125991821 is also prime.
%t Select[LinearRecurrence[{1,1,1},{1,1,1},200],AllTrue[{#,IntegerReverse[ #]},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jul 31 2019 *)
%Y Cf. A000040, A000045, A000213, A004086, A006567, A056816, A115347.
%K more,nonn,base
%O 1,1
%A _Jonathan Vos Post_, Feb 15 2009