A356791 - OEIS

%I #55 Sep 24 2022 21:51:04

%S 13,17,107,149,337,1009,1069,1109,1409,1499,1559,3257,3347,3407,3467,

%T 3527,3697,3767,10009,10429,10739,10859,10939,11057,11149,11159,11257,

%U 11497,11657,11677,11717,11897,11959,13759,13829,14029,14479,14549,15149,15299,15649,30367,30557,31267,31307,32257

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

%C All terms start with digit 1 or 3.

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

%H Robert Israel, <a href="/A356791/b356791.txt">Table of n, a(n) for n = 1..10000</a>

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

%p rev:= proc(n) local K,i;

%p   K:= convert(n,base,10);

%p   add(K[-i]*10^(i-1),i=1..nops(K))

%p end proc:

%p filter:= proc(p) local q;

%p   if not isprime(p) then return false fi;

%p   q:= rev(p);

%p   q > p and isprime(q) and isprime(q mod p)

%p end proc:

%p select(filter, [seq(i,i=3..10^5,2)]);

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

%o (Python)

%o from sympy import isprime

%o def ok(n):

%o     r = int(str(n)[::-1])

%o     return r > n and isprime(n) and isprime(r) and isprime(r%n)

%o print([k for k in range(10**5) if ok(k)]) # _Michael S. Branicky_, Sep 18 2022

%Y Cf. A004086, A006567, A109308.

%K nonn,base

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Sep 18 2022