|
| |
|
|
A059756
|
|
Erdos-Woods numbers: the length of an interval of consecutive integers with property that every element has a factor in common with one of the end-points.
|
|
2
| |
|
|
16, 22, 34, 36, 46, 56, 64, 66, 70, 76, 78, 86, 88, 92, 94, 96, 100, 106, 112, 116, 118, 120, 124, 130, 134, 142, 144, 146, 154, 160, 162, 186, 190, 196, 204, 210, 216, 218, 220, 222, 232, 238, 246, 248, 250, 256, 260, 262, 268, 276, 280, 286, 288, 292, 296, 298, 300, 302, 306, 310, 316, 320, 324, 326, 328, 330, 336, 340, 342, 346, 356, 366, 372, 378, 382, 394, 396, 400, 404, 406, 408, 414, 416, 424, 426, 428, 430
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| "Length" means total number of terms including end-points, minus 1.
Woods was the first to find such numbers, Dowe proved there are infinitely many and Cegielski, Heroult and Richard showed that the set is recursive.
|
|
|
REFERENCES
| P. Cegielski, F. Heroult, D. Richard: On the amplitude of intervals of natural numbers whose every element is coprime with no extremety. 2000
D. Dowe: On the existence of sequences of coprime pairs of integers. J. Austral. Math. Soc. Ser. A 47, no. 1, 84-89. 1989
P. Erdos and J. L. Selfridge: Complete prime subsets of consecutive integers. Proceedings of the Manitobe Conference on Numerical Mathematics. pp. 1-14, 1971
R. K. Guy: Unsolved Problems in Number Theory, 1981, related to Sections B27, B28, B29.
Konstantin Lakkis, Number Theory [in Greek], Revised edition, 1984.
Alan Robert Woods, Some Problems in Logic and Number Theory, and their Connections Thesis, University of Manchester, 1981
|
|
|
LINKS
| Nik Lygeros, Erdos-Woods Numbers
|
|
|
EXAMPLE
| a(1) = 16 refers to the interval 2184, 2185, ..., 2200.
|
|
|
CROSSREFS
| See A059757 for first terms of corresponding intervals. Cf. A111042.
Sequence in context: A064804 A102944 A058901 * A154877 A165338 A100999
Adjacent sequences: A059753 A059754 A059755 * A059757 A059758 A059759
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Nik Lygeros (webmaster(AT)lygeros.org), Feb 12 2001
|
|
|
EXTENSIONS
| Further terms from Victor Miller, Sep 29, 2005
|
| |
|
|
