A115347 -id:A115347 - cp's OEIS frontend

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

3, 5, 17, 31, 1201, 128199521

Offset: 1

Jonathan Vos Post, Feb 15 2009

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

			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.

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

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

{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}.

A173620 Main diagonal of array A[k,n] = n-th Fibonacci number which becomes prime when digits (base k) are reversed.

Original entry on oeis.org

2, 5, 13, 8, 89, 233, 233, 1597, 39088169, 121393, 4052739537881

Offset: 1

Jonathan Vos Post, Feb 22 2010

First row is the prime Fibonacci numbers A005478 (as reverse of unary does not change the number). 10th row is A173268. Computations mostly by R. J. Mathar after first few terms from Jonathan Vos Post. Mathar also notes that omitting the base=1 row, gives the diagonal: 3, 5, 5, 55, 34, 89, 610, 1346269, 75025, 2504730781961, 14930352. The array begins:
===============================================================================
....|.n=1.|.n=2.|.n=3.|.n=4.|.n=5.|.n=6.|.....n=7.|...n=8.|........n=9.|......n=10|
k=1.|..2...|..3.|...5.|..13.|..89.|.233.|....1597.|...28657.|...514229.|.433494437|
k=2.|..3...|..5.|..13.|..34.|..55.|.233.|.....377.|.....610.|.....2584.|...4181657|
k=3.|..2...|..5.|..13.|..21.|..55.|.233.|.....987.|...28657.|....75025.|.433494437|
k=4.|..2...|..3.|...5.|...8.|..13.|..89.|.....233.|....1597.|.....4181.|....514229|
k=5.|..2...|..3.|..13.|..55.|..89.|.233.|...28657.|...21393.|...514229.|...9227465|
k=6.|..2...|..3.|...5.|...8.|..34.|.233.|14930352.|63245986.|701408733|...86267571272.
k=7.|..2...|..3.|...5.|..13.|..21.|..89.|.....233.|....1597.|.....4181|....2865
k=8.|..2...|..3.|...5.|..13.|..89.|.233.|.....610.|....1597.|.....2584|.....4181
k=9.|..2...|..3.|...5.|..13.|..21.|.987.|....1597.|..346269.|.39088169|701408733
k=10|..2...|..3.|...5.|..13.|..34.|.377.|....1597.|...10946.|....75025|121393|
k=11|.2..3....5.....13.....55......89.......233.........1597..956722026041.2504730781961.4052739537881
k=12|.2..3....5.....13.....21......89......1597......1346269......3524578.......5702887.....14930352.4052739537881.
k=13|.2..3....5.....55.....89.....233.......377.........1597........75025.
k=14|.2..3....5.....13...2584....4181..39088169.365435296162.956722026041.
k=15|.2..3....5.....13....233.....377......1597.........4181.........6765.........75025.......121393....701408733.956722026041

Cf. A000040, A000045, A001605, A004086, A115347, A173268.

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

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