A156761 Tribonacci primes that are also primes when their digits are reversed.

3, 5, 17, 31, 1201, 128199521

Offset

1,1

Comments

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.

a(7), if it exists, is greater than A000213(10000). - Dmitry Kamenetsky, Mar 03 2009

a(7), if it exists, is greater than A000213(116404), testing tribonacci primes using A157611. - Michael S. Branicky, May 27 2025

Links

Table of n, a(n) for n=1..6.

Formula

{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}.

Example

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.

Mathematica

Select[LinearRecurrence[{1, 1, 1}, {1, 1, 1}, 200], AllTrue[{#, IntegerReverse[ #]}, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 31 2019 *)

Crossrefs

Cf. A000040, A000045, A000213, A004086, A006567, A056816, A115347, A157611.

Sequence in context: A372012 A007802 A056816 * A371927 A151261 A148504

Adjacent sequences: A156758 A156759 A156760 * A156762 A156763 A156764

Keyword

more,nonn,base

Author

Jonathan Vos Post, Feb 15 2009

Status

approved