A343703 Numbers k such that k=x*y for some x and y such that x+y and the concatenation of x and y are both prime.

1, 4, 6, 10, 12, 18, 22, 24, 28, 30, 40, 42, 46, 48, 52, 54, 58, 60, 66, 70, 72, 76, 78, 82, 84, 88, 90, 102, 106, 112, 114, 126, 130, 132, 136, 138, 142, 148, 150, 154, 156, 162, 168, 172, 180, 184, 186, 190, 192, 196, 198, 204, 208, 210, 220, 222, 228, 232, 238, 246, 252, 258, 262, 268, 274

Offset

1,2

Comments

All terms except 1 are even.

Includes p-1 if p is a prime such that 10*p-9 is prime.

Links

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

Example

a(5) = 12 is a term because 12 = 4*3 where both 43 and 4+3=7 are prime.

Maple

filter:= proc(m) local d, e;
   for d in numtheory:-divisors(m) do
     e:= m/d;
     if isprime(d*10^(1+ilog10(e))+e) and isprime(d+e) then return true fi
   od;
   false
end proc:
select(filter, [$1..1000]);

Crossrefs

Sequence in context: A108724 A243864 A024995 * A086298 A144761 A295523

Adjacent sequences: A343700 A343701 A343702 * A343704 A343705 A343706

Keyword

nonn,base

Author

J. M. Bergot and Robert Israel, Apr 26 2021

Status

approved