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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).
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%I #31 Dec 23 2022 07:38:00

%S 1,105263157894736842,1034482758620689655172413793,102564,142857,

%T 1016949152542372881355932203389830508474576271186440677966,

%U 1014492753623188405797,1012658227848,10112359550561797752808988764044943820224719

%N 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).

%C 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.

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

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Parasitic_number">Parasitic numbers</a> [From Dzmitry Paulenka (pavlenko(AT)tut.by), Aug 09 2009]

%H P. Yiu, <a href="http://math.fau.edu/yiu/RecreationalMathematics2003.pdf">k-left-transposable integers</a>, Chap.18.2 pp. 168/360 in 'Recreational Mathematics'

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

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

%Y Cf. A094676, A081463.

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

%K fini,full,base,nonn

%O 1,2

%A _Lekraj Beedassy_, Aug 21 2004; corrected Dec 17 2004

%E Edited by _N. J. A. Sloane_, Apr 13 2009

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

%E a(9) added by _Ian Duff_, Jan 03 2012

%E Incorrect formula removed by _Alois P. Heinz_, Feb 18 2020