A340843 Emirps p such that p+(sum of digits of p) and reverse(p)+(sum of digits of p) are emirps.

1933, 3391, 32687, 78623, 104087, 109891, 112103, 120283, 123127, 135469, 136217, 161983, 162209, 162391, 163819, 179779, 193261, 198613, 198901, 301211, 316819, 316891, 382021, 389161, 712631, 721321, 726487, 738349, 780401, 784627, 902261, 918361, 918613, 943837, 964531, 977971, 1002247

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

a(3) = 32687 is an emirp because 32687 and 78623 are distinct primes. The sum of digits of 32687 is 26. 32687+26 = 32713 and 78623+26 = 78649 are emirps because 32713 and 31723 are distinct primes, as are 78649 and 94687.

Maple

revdigs:= proc(n) local L, i;
  L:= convert(n, base, 10);
  add(10^(i-1)*L[-i], i=1..nops(L))
end proc:
filter:= proc(n) local r, t, n2, n3;
if not isprime(n) then return false fi;
r:= revdigs(n);
if r = n or not isprime(r) then return false fi;
t:= convert(convert(n, base, 10), `+`);
for n2 in [n+t, r+t] do
  if not isprime(n2) then return false fi;
  r:= revdigs(n2);
  if r = n2 or not isprime(r) then return false fi;
od;
true
end proc:
select(filter, [seq(i, i=13..10^6, 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):
  if not emirp(n): return False
  if not emirp(n + sd(n)): return False
  revn = int(str(n)[::-1])
  return emirp(revn + sd(revn))
def aupto(nn): return [m for m in range(1, nn+1) if ok(m)]
print(aupto(920000)) # Michael S. Branicky, Jan 24 2021

Crossrefs

Cf. A006567. Contained in A340842.

Sequence in context: A227491 A277943 A251945 * A270265 A237010 A256765

Adjacent sequences: A340840 A340841 A340842 * A340844 A340845 A340846

Keyword

nonn,base

Author

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

Status

approved