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).

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

Offset: 1

Author

Lekraj Beedassy, Aug 21 2004; corrected Dec 17 2004

Keywords

• fini
• full
• base
• nonn

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.

Examples

			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]
		

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'

Crossrefs

Cf. A094676, A081463.

For other sequences with the same start, see A128857 and especially the cross-references in A097717.

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