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

1,1

Links

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

Example

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.

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)]);

Prog

(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

Crossrefs

Cf. A006567. Contains A340843.

Sequence in context: A031442 A066831 A067382 * A253776 A158941 A128003

Adjacent sequences: A340839 A340840 A340841 * A340843 A340844 A340845

Keyword

nonn,base

Author

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

Status

approved