A355651 Emirps p such that (p*q) mod (p+q) is also an emirp, where q is the digit reversal of p.

389, 709, 907, 983, 1669, 3163, 3613, 7349, 9349, 9437, 9439, 9661, 11071, 11959, 12841, 13513, 13751, 13757, 13873, 14549, 14593, 14713, 14821, 14923, 15013, 15731, 15919, 16573, 16937, 17011, 17681, 18133, 18671, 30197, 31051, 31531, 31741, 32579, 32783, 32941, 33181, 33287, 35129, 36217, 37561

Offset

1,1

Comments

If p is a term, so is A004086(p).

Links

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

Example

a(3) = 907 is a term because 907 and its digit reversal 709 are distinct primes, and (907*709) mod (907 + 709) = 1511 and its digit reversal 1151 are distinct primes.

Maple

rev:= proc(n) local L, i;
  L:= convert(n, base, 10);
  add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
filter:= proc(p) local q, r, s;
if not isprime(p) then return false fi;
q:= rev(p);
if q=p or not isprime(q) then return false fi;
r:= (p*q) mod (p+q);
if not isprime(r) then return false fi;
s:= rev(r);
s <> r and isprime(s)
end proc:
select(filter, [seq(i, i=13..10^5, 2)]);

Mathematica

emirpQ[p_] := (r = IntegerReverse[p]) != p && PrimeQ[p] && PrimeQ[r]; Select[Range[40000], emirpQ[#] && emirpQ[Mod[#*(r = IntegerReverse[#]), # + r]] &] (* Amiram Eldar, Sep 04 2022 *)

Prog

(Python)
from sympy import isprime
def emirp(n):
    revn = int(str(n)[::-1])
    return n != revn and isprime(n) and isprime(revn)
def ok(n):
    if not emirp(n): return False
    q = int(str(n)[::-1])
    return emirp((n*q)%(n+q))
print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, Sep 04 2022

Crossrefs

Cf. A004086, A006567, A356740.

Sequence in context: A052377 A154624 A052353 * A257119 A298238 A299364

Adjacent sequences: A355648 A355649 A355650 * A355652 A355653 A355654

Keyword

nonn,base,less

Author

J. M. Bergot and Robert Israel, Sep 04 2022

Status

approved