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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).
13
1, 105263157894736842, 1034482758620689655172413793, 102564, 142857, 1016949152542372881355932203389830508474576271186440677966, 1014492753623188405797, 1012658227848, 10112359550561797752808988764044943820224719
OFFSET
1,2
COMMENTS
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.
REFERENCES
C. A. Pickover, Wonders of Numbers, Chapter 28, Oxford Univ. Press UK 2000.
LINKS
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'
EXAMPLE
102564 is 4-parasitic because we have 102564*4=410256.
For n=5: 142857*5=714285. [Dzmitry Paulenka (pavlenko(AT)tut.by), Aug 09 2009]
CROSSREFS
For other sequences with the same start, see A128857 and especially the cross-references in A097717.
Sequence in context: A267076 A146088 A217592 * A097717 A128857 A357515
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 5-parasitic number. Dzmitry Paulenka (pavlenko(AT)tut.by), Aug 09 2009
a(9) added by Ian Duff, Jan 03 2012
Incorrect formula removed by Alois P. Heinz, Feb 18 2020
STATUS
approved