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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; text; 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

Table of n, a(n) for n=1..87.

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

STATUS

approved

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Last modified April 19 00:07 EDT 2014. Contains 240735 sequences.