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A031217
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Number of terms in longest arithmetic progression of consecutive primes starting at n-th prime (conjectured to be unbounded).
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1
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2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n) <=4 for n <=100000. - Reinhard Zumkeller, Feb 02 2007
The first instance of 4 consecutive primes in an arithmetic progression is (251, 257, 263, 269), which starts with the 54th prime. The first instance of 5 consecutive primes in an arithmetic progression is (9843019, 9843049, 9843079, 9843109, 9843139), which starts with the 654926th prime. [From Harvey P. Dale, Jul 13 2011]
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REFERENCES
| R. K. Guy, Unsolved Problems in Number Theory, A6.
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences related to primes in arithmetic progressions
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EXAMPLE
| At 47 there are 3 consecutive primes in A.P., 47 53 59.
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CROSSREFS
| Cf. A001223.
Sequence in context: A090387 A030329 A120881 * A078545 A111497 A097051
Adjacent sequences: A031214 A031215 A031216 * A031218 A031219 A031220
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu)
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