A358689 Emirps p such that 2*p - reverse(p) is also an emirp.

941, 1031, 1201, 1471, 7523, 7673, 7687, 9133, 9293, 9479, 9491, 9601, 9781, 9923, 10091, 10711, 12071, 14891, 15511, 17491, 17681, 18671, 32633, 33623, 34963, 35983, 36943, 36973, 37963, 39157, 70913, 72253, 72337, 72353, 73327, 74093, 75223, 75577, 75833, 75913, 77263, 77557, 79393, 79973

Offset

1,1

Links

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

Example

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.

Maple

rev:= proc(n) local L, t;
  L:= convert(n, base, 10);
  add(L[-t]*10^(t-1), t=1..nops(L));
end proc:
filter:= proc(n) local r, s, t;
   if not isprime(n) then return false fi;
   r:= rev(n);
   if r = n or not isprime(r) then return false fi;
   s:= 2*n-r;
   if not isprime(s) then return false fi;
   t:= rev(s);
   t <> s and isprime(t)
end proc:
select(filter, [seq(i, i=3..100000, 2)]);

Mathematica

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 *)

Crossrefs

Cf. A006567.

Sequence in context: A259641 A200428 A104917 * A052238 A158718 A104302

Adjacent sequences: A358686 A358687 A358688 * A358690 A358691 A358692

Keyword

nonn,base

Author

J. M. Bergot and Robert Israel, Dec 08 2022

Status

approved