A383195 Primes that are the concatenation of three primes, of which two are equal.

223, 227, 233, 277, 337, 353, 373, 557, 577, 727, 733, 757, 773, 1733, 1777, 1933, 2213, 2237, 2243, 2267, 2273, 2297, 2333, 2377, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3413, 3433, 3533, 3593, 3613, 3673, 3733, 3793, 3833, 4133, 4177, 4733, 5333, 5519, 5531, 5573

Offset: 1

Author

Robert Israel, Apr 28 2025

Keywords

• nonn

Comments

Complement of A100633 in A100607.

Examples

			a(3) = 233 is a term because 233 is prime and is the concatenation of the primes 2, 3 and 3, of which two are equal.
		

Links

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

Crossrefs

Cf. A100607, A100633.

Programs

Maple

filter:= proc(n) local m, i, j, ni, nj, np, n3;
 if not isprime(n) then return false fi;
 m:= ilog10(n);
 for i from 1 to m-1 do
   ni:= n mod 10^i;
   if ni < 10^(i-1) or not isprime(ni) then next fi;
   np:= (n-ni)/10^i;
   for j from 1 to m-i do
     nj:= np mod 10^j;
     if nj < 10^(j-1) then next fi;
     n3:= (np-nj)/10^j;
     if nops({ni, nj, n3})<3 and isprime(nj) and isprime(n3) then return true fi;
 od od;
 false
end proc:
select(filter, [seq(i,i=3..10000,2)]);