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A340843
Emirps p such that p+(sum of digits of p) and reverse(p)+(sum of digits of p) are emirps.
2
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
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
KEYWORD
nonn,base
AUTHOR
J. M. Bergot and Robert Israel, Jan 23 2021
STATUS
approved