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 A100607 Concatenated primes of order 3. 5
 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 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] (from Robert G. Wilson v Dec 03 2004) CROSSREFS Cf. A019549. Sequence in context: A178551 A105982 A153424 * A092623 A220474 A098591 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

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