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A117646
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Sets of three primes with equal gaps: ( Martian Primes) Prime[n]+2*m=Prime[n+1] Prime[n+1]+2*m=Prime[n+2] A Goedel prime equivalent to if A Implies B and B implies C then A Implies C.
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0
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3, 5, 7, 47, 53, 59, 151, 157, 163, 167, 173, 179, 199, 211, 223, 251, 257, 263, 257, 263, 269, 367, 373, 379, 557, 563, 569, 587, 593, 599, 601, 607, 613, 647, 653, 659, 727, 733, 739, 941, 947, 953, 971, 977, 983, 1097, 1103, 1109, 1117, 1123, 1129, 1181
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| In H.G. Wells' War of the Worlds the Martians use a base three number system: in such a system 3^n+2 instead of 2^n+1 primes would be inportant. Likewise instead of pairs of primes, triplets of primes would be studied as "interesting", so I call these Martian Prime triples as that's what gave me the idea for finding them.
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REFERENCES
| http://en.wikipedia.org/wiki/The_War_of_the_Worlds_(1953_movie) http://en.wikipedia.org/wiki/The_War_of_the_Worlds_(novel)
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FORMULA
| a(n) =If gap=2*m then { Prime[n],Prime[n+1],Prime[n+2]}
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MATHEMATICA
| a = Delete[Union[Flatten[Table[If[(Prime[n] + 2*m - Prime[n + 1] == 0) && (Prime[n + 1] + 2*m - Prime[ n + 2] == 0), {Prime[n], Prime[n + 1], Prime[ n + 2]}, {}], {m, 1, 17}, {n, 1, 200}], 1]], 1] Flatten[a]
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CROSSREFS
| Sequence in context: A146972 A102742 A089044 * A064857 A065913 A137999
Adjacent sequences: A117643 A117644 A117645 * A117647 A117648 A117649
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 10 2006
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