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A358689
Emirps p such that 2*p - reverse(p) is also an emirp.
2
941, 1031, 1201, 1471, 7523, 7673, 7687, 9133, 9293, 9479, 9491, 9601, 9781, 9923, 10091, 10711, 12071, 14891, 15511, 17491, 17681, 18671, 32633, 33623, 34963, 35983, 36943, 36973, 37963, 39157, 70913, 72253, 72337, 72353, 73327, 74093, 75223, 75577, 75833, 75913, 77263, 77557, 79393, 79973
OFFSET
1,1
LINKS
EXAMPLE
a(3) = 1201 is a term because it is an emirp, i.e., 1201 and its reverse 1021 are distinct primes, and 2*1201 - 1021 = 1381 is also an emirp.
MAPLE
rev:= proc(n) local L, t;
L:= convert(n, base, 10);
add(L[-t]*10^(t-1), t=1..nops(L));
end proc:
filter:= proc(n) local r, s, t;
if not isprime(n) then return false fi;
r:= rev(n);
if r = n or not isprime(r) then return false fi;
s:= 2*n-r;
if not isprime(s) then return false fi;
t:= rev(s);
t <> s and isprime(t)
end proc:
select(filter, [seq(i, i=3..100000, 2)]);
MATHEMATICA
emirpQ[n_] := ! PalindromeQ[n] && AllTrue[{n, IntegerReverse[n]}, PrimeQ]; q[n_] := emirpQ[n] && (d = 2*n - IntegerReverse[n]) > 0 && AllTrue[{d, IntegerReverse[d]}, emirpQ]; Select[Range[80000], q] (* Amiram Eldar, Dec 08 2022 *)
CROSSREFS
Cf. A006567.
Sequence in context: A259641 A200428 A104917 * A052238 A158718 A104302
KEYWORD
nonn,base
AUTHOR
J. M. Bergot and Robert Israel, Dec 08 2022
STATUS
approved