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A100607
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Concatenated primes of order 3.
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5
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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; internal format)
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OFFSET
| 1,1
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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
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LINKS
| Chris Caldwell, The First thousand primes.
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FORMULA
| Each of the listed primes is made from three primes (same or different).
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EXAMPLE
| 257 is in the sequence since it is made from three (distinct) primes.
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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)
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CROSSREFS
| Cf. A019549.
Sequence in context: A178551 A105982 A153424 * A092623 A098591 A152824
Adjacent sequences: A100604 A100605 A100606 * A100608 A100609 A100610
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KEYWORD
| easy,nonn,base
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AUTHOR
| Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Nov 30 2004
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EXTENSIONS
| Corrected and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 03 2004
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