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

1,2

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

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'

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

Cf. A094676, A081463.

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

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 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