A100607 - OEIS

%I #8 Mar 14 2015 18:40:59

%S 223,227,233,257,277,337,353,373,523,557,577,727,733,757,773,1123,

%T 1153,1327,1373,1723,1733,1753,1777,1933,1973,2113,2137,2213,2237,

%U 2243,2267,2273,2293,2297,2311,2333,2341,2347,2357,2371,2377,2383,2389,2417,2437

%N Concatenated primes of order 3.

%C This is a subset of all concatenated primes (A019549). Some of these primes have dual order - example 223. It can be viewed as order two(2 and 23) or as order three (2,2 and 3).

%C There are 15 such numbers less than 1000 and 202 less than 10^4. - _Robert G. Wilson v_, Dec 03 2004

%H Chris Caldwell, <a href="http://www.utm.edu/research/primes/lists/small/1000.txt">The First thousand primes</a>.

%F Each of the listed primes is made from three primes (same or different).

%e 257 is in the sequence since it is made from three (distinct) primes.

%t (* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) t = Sort[ KSubsets[ Flatten[ Table[ Prime[ Range[25]], {3}]], 3]]; lst = {}; Do[k = 1; u = Permutations[t[[n]]]; While[k < Length[u], v = FromDigits[ Flatten[ IntegerDigits /@ u[[k]]]]; If[ PrimeQ[v], AppendTo[lst, v]]; k++ ], {n, Length[t]}]; Take[ Union[lst], 45] (* _Robert G. Wilson v_, Dec 03 2004 *)

%Y Cf. A019549.

%K easy,nonn,base

%O 1,1

%A _Parthasarathy Nambi_, Nov 30 2004

%E Corrected and extended by _Robert G. Wilson v_, Dec 03 2004