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A092697 For 1 <= n <= 9, a(n) = least number m such that the product n*m is obtained merely by shifting the rightmost digit of m to the left end (a finite sequence). 5
1, 105263157894736842, 1034482758620689655172413793, 102564, 142857, 1016949152542372881355932203389830508474576271186440677966, 1014492753623188405797, 1012658227848, 10112359550561797752808988764044943820224719 (list; graph; refs; listen; history; text; internal format)



This is the least n-parasitic number. A k-parasitic number (where 1 <= k <= 9) is one such that when it is multiplied by k, the product obtained is merely its rightmost digit transferred in front at the leftmost end.

By accident, the nine terms of this sequence coincide with the first nine terms of the infinite sequence A128857. - N. J. A. Sloane, Apr 13 2009


C. A. Pickover, Wonders of Numbers, Chapter 28, Oxford Univ. Press UK 2000.


Table of n, a(n) for n=1..9.

Wikipedia, Parasitic numbers [From Dzmitry Paulenka (pavlenko(AT)tut.by), Aug 09 2009]

P. Yiu, k-left-transposable integers, Chap.18.2 pp. 168/360 in 'Recreational Mathematics'


a(n) = n(10^m-1)/(10n-1), where m (=A094224) is the order of 10 modulo 10n-1. - Moses Liskov (mliskov(AT)cs.wm.edu), May 17 2006


102564 is 4-parasitic because we have 102564*4=410256.

For n=5: 142857*5=714285 [From Dzmitry Paulenka (pavlenko(AT)tut.by), Aug 09 2009]


Cf. A094676.

Cf. A081463, A097717, A128857. [From R. J. Mathar, Mar 30 2009]

Sequence in context: A267076 A146088 A217592 * A097717 A128857 A246111

Adjacent sequences:  A092694 A092695 A092696 * A092698 A092699 A092700




Lekraj Beedassy, Aug 21 2004; corrected Dec 17 2004


Edited by N. J. A. Sloane, Apr 13 2009

Corrected to set 5th term to 142857 as this is the least 5-parasitic number. Dzmitry Paulenka (pavlenko(AT)tut.by), Aug 09 2009

a(9) added by Ian Duff, Jan 03 2012



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Last modified May 29 03:28 EDT 2017. Contains 287242 sequences.