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Search: id:A100607
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| A100607 |
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Concatenated primes of order 3. |
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+0
6
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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; listen)
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OFFSET
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1,1
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COMMENT
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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
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Chris Caldwell, The First thousand primes.
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FORMULA
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Each of the listed primes is made from three primes (same or different).
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EXAMPLE
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257 is in the sequence since it is made from three (distinct) primes.
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MATHEMATICA
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(* 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
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Cf. A019549.
Adjacent sequences: A100604 A100605 A100606 this_sequence A100608 A100609 A100610
Sequence in context: A063352 A043499 A105982 this_sequence A092623 A098591 A102950
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KEYWORD
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easy,nonn
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AUTHOR
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Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Nov 30 2004
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EXTENSIONS
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Corrected and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 03 2004
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