A345191 a(n) is the least emirp k such that 2*n-k is also an emirp, or 0 if there are none.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 13, 0, 17, 0, 0, 0, 0, 13, 0, 17, 13, 0, 17, 0, 0, 0, 31, 0, 0, 31, 0, 0, 37, 0, 0, 0, 0, 13, 13, 17, 17, 13, 0, 17, 0, 0, 31, 31, 0, 37, 13, 0, 17, 37, 0, 13, 0, 17, 13, 31, 17, 0, 37, 0, 31, 0, 71, 31, 73, 0, 37, 73, 0, 0, 79, 0, 13, 0, 17, 71, 13, 0

Offset

1,13

Links

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

Example

a(24) = 17 because 2*24 = 17+31 where 17 and 31 are emirps.

Maple

revdigs:= proc(n) local L, i;
  L:= convert(n, base, 10);
  add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
filter:= proc(t) local r;
if not isprime(t) then return false fi;
r:= revdigs(t);
r <> t and isprime(r)
end proc:
N:= 1000: # for a(1)..a(N)
E:= select(filter, [seq(i, i=3..2*N, 2)]);
f:= proc(n) local i, j, w, t;
  t:= 2*n;
  j:= ListTools:-BinaryPlace(E, t);
  i:= 1;
  while i <= j do
    w:= E[i]+E[j];
    if w = t then return E[i]
    elif w < t then i:=i+1
    else j:= j-1
    fi
  od;
  0
end proc:
map(f, [$1..N]);

Crossrefs

Cf. A006567

Sequence in context: A221341 A221106 A271075 * A073867 A114782 A065112

Adjacent sequences: A345188 A345189 A345190 * A345192 A345193 A345194

Keyword

nonn,base,look

Author

J. M. Bergot and Robert Israel, Jun 10 2021

Status

approved