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Search: id:A088430
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| A088430 |
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a(n) = the least positive d such that for p=prime(n), the numbers p+0d, p+1d, p+2d, ..., p+(p-1)d are all primes. See A113834 for last term in the progression. |
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6
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| 1, 2, 6, 150, 1536160080, 9918821194590, 341976204789992332560
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Problem discussed by Russell E. Rierson: starting with given p, find the least d such that the arithmetic progression p,p+d,p+2d,... contains only primes. Obviously, the maximum number of prime terms is p, and to reach that maximum, d must be a multiple of all smaller primes. For example, a(5) is a multiple of 2*3*5*7.
There can be other maximum-length prime progressions starting at p, with larger d. (Zak Seidov found d=4911773580 for p=11.)
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LINKS
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Phil Carmody, a(7)
Andrew Granville, Prime number patterns
Ben Green and Terence Tao, The primes contain arbitrarily long arithmetic progressions [Background]
Russell E. Rierson, Question About Prime Numbers.
Zak Seidov, Question About Prime Numbers.
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EXAMPLE
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n AP Last term
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2 2+i 3
3 3+2*i 7
5 5+6*i 29
7 7+150*i 907
11 11+1536160080*i 15361600811
13 13+9918821194590*i 119025854335093
17 17+341976204789992332560*i 5471619276639877320977
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CROSSREFS
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Cf. A113836.
Adjacent sequences: A088427 A088428 A088429 this_sequence A088431 A088432 A088433
Sequence in context: A024397 A015173 A122570 this_sequence A051240 A003189 A135937
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KEYWORD
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more,nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Sep 30 2003
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EXTENSIONS
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Edited by Don Reble (djr(AT)nk.ca), Oct 04 2003
a(7) was found by Phil Carmody. - Don Reble (djr(AT)nk.ca), Nov 23 2003
Entry revised by njas, Jan 25 2006
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