A358689 - OEIS

%I #29 Dec 11 2022 01:34:07

%S 941,1031,1201,1471,7523,7673,7687,9133,9293,9479,9491,9601,9781,9923,

%T 10091,10711,12071,14891,15511,17491,17681,18671,32633,33623,34963,

%U 35983,36943,36973,37963,39157,70913,72253,72337,72353,73327,74093,75223,75577,75833,75913,77263,77557,79393,79973

%N Emirps p such that 2*p - reverse(p) is also an emirp.

%H Robert Israel, <a href="/A358689/b358689.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 1201 is a term because it is an emirp, i.e., 1201 and its reverse 1021 are distinct primes, and 2*1201 - 1021 = 1381 is also an emirp.

%p rev:= proc(n) local L,t;

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

%p   add(L[-t]*10^(t-1),t=1..nops(L));

%p end proc:

%p filter:= proc(n) local r,s,t;

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

%p    r:= rev(n);

%p    if r = n or not isprime(r) then return false fi;

%p    s:= 2*n-r;

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

%p    t:= rev(s);

%p    t <> s and isprime(t)

%p end proc:

%p select(filter, [seq(i,i=3..100000,2)]);

%t emirpQ[n_] := ! PalindromeQ[n] && AllTrue[{n, IntegerReverse[n]}, PrimeQ]; q[n_] := emirpQ[n] && (d = 2*n - IntegerReverse[n]) > 0 && AllTrue[{d, IntegerReverse[d]}, emirpQ]; Select[Range[80000], q] (* _Amiram Eldar_, Dec 08 2022 *)

%Y Cf. A006567.

%K nonn,base

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Dec 08 2022