

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
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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

Table of n, a(n) for n=1..45.
Chris Caldwell, The First thousand primes.


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

Cf. A019549.
Sequence in context: A105982 A243766 A153424 * A092623 A220474 A243767
Adjacent sequences: A100604 A100605 A100606 * A100608 A100609 A100610


KEYWORD

easy,nonn,base


AUTHOR

Parthasarathy Nambi, Nov 30 2004


EXTENSIONS

Corrected and extended by Robert G. Wilson v, Dec 03 2004


STATUS

approved



