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Search: id:A113833
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| A113833 |
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Triangle read by rows: row n (n>=2) gives a set of n primes with the property that the averages of all subsets are distinct primes, having the smallest largest element. |
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3
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| 3, 7, 7, 19, 67, 5, 17, 89, 1277, 209173, 322573, 536773, 1217893, 2484733
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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If there is more than one set with the same smallest last element, choose the lexicographically earliest solution.
Note that, in each row, the n primes are equal modulo 4, 12, 12 and 120, respectively. - Row 5 from T. D. Noe (noe(AT)sspectra.com), Aug 08 2006
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REFERENCES
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Antal Balog, The prime k-tuplets conjecture on average, in ``Analytic Number Theory'' (eds. B. C. Berndt et al) Birkh\"auser, Boston, 1990, pp. 165-204. [Background]
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LINKS
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Jens Kruse Andersen, Primes in Arithmetic Progression Records [May have candidates for later terms in this sequence.]
Andrew Granville, Prime number patterns
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EXAMPLE
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Triangle begins:
3, 7
7, 19, 67
5, 17, 89, 1277
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CROSSREFS
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Cf. A113827-A113831, A113832, A113834, A088430.
Sequence in context: A130003 A098581 A085420 this_sequence A121172 A077629 A004794
Adjacent sequences: A113830 A113831 A113832 this_sequence A113834 A113835 A113836
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KEYWORD
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nonn,tabf,more
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AUTHOR
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njas, Jan 25 2006
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EXTENSIONS
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Row 5 from T. D. Noe (noe(AT)sspectra.com), Aug 08 2006
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