

A059756


ErdosWoods numbers: the length of an interval of consecutive integers with property that every element has a factor in common with one of the endpoints.


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
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OFFSET

1,1


COMMENTS

"Length" means total number of terms including endpoints, 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, 8489. 1989
P. Erdos and J. L. Selfridge: Complete prime subsets of consecutive integers. Proceedings of the Manitobe Conference on Numerical Mathematics. pp. 114, 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, ErdosWoods 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



