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

1,1

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.

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A004086, A006567, A109308.

Sequence in context: A108265 A069853 A175791 * A289866 A210547 A202136

Adjacent sequences: A356788 A356789 A356790 * A356792 A356793 A356794

Keyword

nonn,base

Author

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

Status

approved