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| A059756
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Erdős-Woods numbers: the length of an interval of consecutive integers with property that every element has a factor in common with one of the endpoints.
(history;
published version)
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#88 by Charles R Greathouse IV at Sun Jun 30 16:25:56 EDT 2024
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#87 by Charles R Greathouse IV at Sun Jun 30 16:25:50 EDT 2024
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| PROG
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(PARI) prime_part(n)={my(P=primes(primepi(n-1))); forstep(x1=2, 2^#P-1, 2, P1=vecextract(P, x1); P2=setminus(P, P1); for(n1=1, n-1, bittest(n-n1, 0) || next; setintersect(P1, factor(n1)[, 1]~) || setintersect(P2, factor(n-n1)[, 1]~) || next(2)); return([P1, P2]))} \\ _M. F. Hasler_, Jun 29 2014
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approved
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#86 by N. J. A. Sloane at Mon Jan 02 12:30:46 EST 2023
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Christopher Hunt Gribble, <a href="http://list.seqfan.eu/pipermail/seqfan/2014-December/014092.html">Seqfan thread</a>, Dec 05 2014.
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Discussion
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| Mon Jan 02
| 12:30
| OEIS Server: https://oeis.org/edit/global/2957
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#85 by Alois P. Heinz at Sun Aug 01 09:08:02 EDT 2021
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#84 by Joerg Arndt at Sun Aug 01 06:44:20 EDT 2021
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#83 by Michel Marcus at Sun Aug 01 05:53:12 EDT 2021
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Discussion
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| Sun Aug 01
| 05:53
| Michel Marcus: Nice typo
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#82 by Michel Marcus at Sun Aug 01 05:52:59 EDT 2021
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| LINKS
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M. F. Hasler and R. J. Mathar, <a href="http://arxiv.org/abs/1510.07997">Corrigendum to "Paths and circuits in finite groups", Discr. Math. 22 (1978) 263</a>, arXiv:1510.07997 (2015).
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proposed
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#81 by David Radcliffe at Sun Aug 01 05:38:39 EDT 2021
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#80 by David Radcliffe at Sun Aug 01 05:37:33 EDT 2021
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| COMMENTS
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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.
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| LINKS
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Alan Robert Woods, <a href="http://school.maths.uwa.edu.au/~woods/thesis/WoodsPhDThesis.pdf">Some Problems in Logic and Number Theory, and their Connections</a>, Thesis, University of Manchester, 1981 (reprinted in New Studies in Weak Arithmetics, Sept 2013, CSLI).
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#79 by David Radcliffe at Sun Aug 01 05:16:53 EDT 2021
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M. F. Hasler and R. J. Mathar, <a href="http://arxiv.org/abs/1510.07997">Corrigendum to "Paths and circutis in finite groups", Discr. Math. 22 (1978) 263</a>, arXiv:1510.07997 (2015).
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approved
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