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Search: id:A059751
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| A059751 |
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Grimm numbers (2): a(n) = largest k so that for each composite m in {n+1, n+2, ..., n+k} there corresponds a different divisor d_m with 1 < d_m < m. |
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+0
3
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| 7, 6, 5, 10, 9, 14, 13, 12, 15, 22, 21, 20, 19, 20, 23, 22, 21, 20, 19, 18, 27, 26, 25, 24, 29, 30, 29, 28, 27, 26, 25, 24, 31, 34, 41, 40, 39, 46, 47, 46, 45, 44, 43, 42, 41, 44, 43, 42
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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C. A. Grimm, A conjecture on consecutive composite numbers, Amer. Math. Monthly, 76 (1969), 1126-1128.
D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section XII.15, p. 438.
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EXAMPLE
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For n=4 we look at the sequence {5, 6, 7, ... } and we must choose distinct proper divisors for as many composites as we can. We can choose 2 for 6, 4 for 8, 3 for 9, 5 for 10, 6 for 12 and 7 for 14, but now all the proper divisors of 15 have appeared, so we stop, and a(4) = 14-4 = 10.
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CROSSREFS
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Cf. A059686, A059752.
Sequence in context: A104178 A092874 A015791 this_sequence A019859 A102769 A031348
Adjacent sequences: A059748 A059749 A059750 this_sequence A059752 A059753 A059754
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas, Feb 11 2001
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EXTENSIONS
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More terms from Naohiro Nomoto (6284968128(AT)geocities.co.jp), Mar 03 2001
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