|
|
A100607
|
|
Concatenated primes of order 3.
|
|
6
|
|
|
223, 227, 233, 257, 277, 337, 353, 373, 523, 557, 577, 727, 733, 757, 773, 1123, 1153, 1327, 1373, 1723, 1733, 1753, 1777, 1933, 1973, 2113, 2137, 2213, 2237, 2243, 2267, 2273, 2293, 2297, 2311, 2333, 2341, 2347, 2357, 2371, 2377, 2383, 2389, 2417, 2437
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
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).
There are 15 such numbers less than 1000 and 202 less than 10^4. - Robert G. Wilson v, Dec 03 2004
|
|
LINKS
|
|
|
FORMULA
|
Each of the listed primes is made from three primes (same or different).
|
|
EXAMPLE
|
257 is in the sequence since it is made from three (distinct) primes.
|
|
MATHEMATICA
|
(* 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 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn,base
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|