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A084337 Rearrangement of natural numbers so that the successive ratios ( of the larger to the smaller term) are all distinct integers. a(m)/a(m-1)= a(k)/a(k-1) iff m = k ( assuming a(m) > a(m-1) otherwise the ratio a(m-1)/a(m) is to be considered). Priority is given to smallest number not included earlier than to the successive ratio that has not occurred earlier. 1
1, 2, 6, 24, 3, 15, 90, 5, 35, 315, 7, 70, 770, 10, 120, 4, 52, 728, 8, 128, 1920, 12, 204, 3876, 17, 340, 7140, 14, 308, 11, 253, 6072, 22, 550, 14300, 13, 351, 9, 261, 8091, 29, 928, 16, 528, 17952, 32, 1120, 20, 720, 18, 666, 25308, 19, 779, 32718, 21, 903, 39732 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The sequence of successive ratios is 2/1,6/2,24/6,24/3,15/3,90/15,90/9,63/9,63/7,... or 2,3,4,8,5,6,10,7,9,...

LINKS

Ivan Neretin, Table of n, a(n) for n = 0..5000

MATHEMATICA

a = r = {1}; Do[If[(ds = Select[Divisors[a[[-1]]], ! MemberQ[a, #] && ! MemberQ[r, a[[-1]]/#] &, 1]) != {}, nxta = ds[[1]]; nxtr = a[[-1]]/nxta, k = 1; While[MemberQ[r, k] || MemberQ[a, a[[-1]]*k], k++]; nxtr = k; nxta = k*a[[-1]]]; AppendTo[a, nxta]; AppendTo[r, nxtr], {n, 57}]; a (* Ivan Neretin, Jul 05 2015 *)

CROSSREFS

Sequence in context: A213324 A007672 A322255 * A204934 A033642 A181952

Adjacent sequences:  A084334 A084335 A084336 * A084338 A084339 A084340

KEYWORD

nonn

AUTHOR

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 18 2003

EXTENSIONS

Corrected and extended by David Wasserman, Dec 15 2004

STATUS

approved

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Last modified March 20 21:49 EDT 2019. Contains 321352 sequences. (Running on oeis4.)