A340842 Emirps p such that p + (sum of digits of p) is an emirp.

13, 71, 97, 701, 1061, 1223, 1597, 1847, 1933, 3067, 3089, 3373, 3391, 3889, 7027, 7043, 7577, 9001, 9241, 9421, 10061, 10151, 10333, 10867, 11057, 11657, 11677, 11897, 11923, 12227, 12269, 12809, 13147, 13457, 13477, 14087, 14207, 16979, 17011, 17033, 17903, 32173, 32203, 32353, 32687, 33589

Offset: 1

Author

J. M. Bergot and Robert Israel, Jan 23 2021

Keywords

• nonn
• base

Examples

			a(3) = 97 is an emirp because 97 and 79 are distinct primes. Its sum of digits is 9+7=16, and 97+16 = 113 is an emirp because 113 and 311 are primes.
		

Links

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

Crossrefs

Cf. A006567. Contains A340843.

Programs

Maple

revdigs:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(10^(i-1)*L[-i],i=1..nops(L))
end proc:
isemirp:= proc(n) local r;
if not isprime(n) then return false fi;
r:= revdigs(n);
r <> n and isprime(r)
end proc:
filter:= n -> isemirp(n) and isemirp(n +convert(convert(n,base,10),`+`)):
select(filter, [seq(i,i=3..10^5,2)]);

Python

from sympy import isprime
def sd(n): return sum(map(int, str(n)))
def emirp(n):
  if not isprime(n): return False
  revn = int(str(n)[::-1])
  if n == revn: return False
  return isprime(revn)
def ok(n): return emirp(n) and emirp(n + sd(n))
def aupto(nn): return [m for m in range(1, nn+1) if ok(m)]
print(aupto(18000)) # Michael S. Branicky, Jan 24 2021