A356791 Emirps p such that R(p) > p and R(p) mod p is prime, where R(p) is the reversal of p.

13, 17, 107, 149, 337, 1009, 1069, 1109, 1409, 1499, 1559, 3257, 3347, 3407, 3467, 3527, 3697, 3767, 10009, 10429, 10739, 10859, 10939, 11057, 11149, 11159, 11257, 11497, 11657, 11677, 11717, 11897, 11959, 13759, 13829, 14029, 14479, 14549, 15149, 15299, 15649, 30367, 30557, 31267, 31307, 32257

Offset: 1

Author

J. M. Bergot and Robert Israel, Sep 18 2022

Keywords

• nonn
• base

Comments

All terms start with digit 1 or 3.

It appears that the only term that does not end with digit 7 or 9 is 13.

Examples

			a(3) = 107 is a term because it is prime, its reversal 701 is prime, and 701 mod 107 = 59 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004086, A006567, A109308.

Programs

Maple

rev:= proc(n) local K,i;
  K:= convert(n,base,10);
  add(K[-i]*10^(i-1),i=1..nops(K))
end proc:
filter:= proc(p) local q;
  if not isprime(p) then return false fi;
  q:= rev(p);
  q > p and isprime(q) and isprime(q mod p)
end proc:
select(filter, [seq(i,i=3..10^5,2)]);

Mathematica

q[p_] := Module[{r = IntegerReverse[p]}, r > p && PrimeQ[r] && PrimeQ[Mod[r, p]]]; Select[Prime[Range[3500]], q] (* Amiram Eldar, Sep 18 2022 *)

Python

from sympy import isprime
def ok(n):
    r = int(str(n)[::-1])
    return r > n and isprime(n) and isprime(r) and isprime(r%n)
print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, Sep 18 2022