

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).


12



1, 105263157894736842, 1034482758620689655172413793, 102564, 142857, 1016949152542372881355932203389830508474576271186440677966, 1014492753623188405797, 1012658227848, 10112359550561797752808988764044943820224719
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OFFSET

1,2


COMMENTS

This is the least nparasitic number. A kparasitic 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


REFERENCES

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


LINKS

Table of n, a(n) for n=1..9.
Wikipedia, Parasitic numbers [From Dzmitry Paulenka (pavlenko(AT)tut.by), Aug 09 2009]
P. Yiu, klefttransposable integers, Chap.18.2 pp. 168/360 in 'Recreational Mathematics'


FORMULA

a(n) = n(10^m1)/(10n1), where m (=A094224) is the order of 10 modulo 10n1.  Moses Liskov (mliskov(AT)cs.wm.edu), May 17 2006


EXAMPLE

102564 is 4parasitic because we have 102564*4=410256.
For n=5: 142857*5=714285 [From Dzmitry Paulenka (pavlenko(AT)tut.by), Aug 09 2009]


CROSSREFS

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


KEYWORD

fini,full,base,nonn


AUTHOR

Lekraj Beedassy, Aug 21 2004; corrected Dec 17 2004


EXTENSIONS

Edited by N. J. A. Sloane, Apr 13 2009
Corrected to set 5th term to 142857 as this is the least 5parasitic number. Dzmitry Paulenka (pavlenko(AT)tut.by), Aug 09 2009
a(9) added by Ian Duff, Jan 03 2012


STATUS

approved



