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

1,1

Comments

Complement of A100633 in A100607.

Links

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

Example

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.

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)]);

Crossrefs

Cf. A100607, A100633.

Sequence in context: A378081 A100607 A092623 * A220474 A243767 A345533

Adjacent sequences: A383192 A383193 A383194 * A383196 A383197 A383198

Keyword

nonn

Author

Robert Israel, Apr 28 2025

Status

approved