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A178303
Smallest multiple of 13 such that decimals digits 1, ..., k (k = 1, ..., 9) and 0 appear in any order.
3
13, 182, 312, 2314, 14235, 125346, 1234675, 12348765, 123456879, 1023457968
OFFSET
1,1
COMMENTS
Divisibility of a number N by 13: add the digits of N in alternate blocks of three from right to left, then subtract the two sums:
9th term: 123 456 879: (123 + 879) - 456 = 546, 546: 54 + (6 * 4) = 78 = 6 * 13.
REFERENCES
Faith Javane, Zahlenmystik: Das Handbuch der Numerologie, Goldmann - Arkana, Frankfurt, 1995
Helmut Kracke, Mathe - musische Knobelisken. Tüfteleien für Tüftler und Laien, Dümmler, Bonn, 1982
Hugo Steinhaus, Kaleidoskop der Mathematik, Deutscher Verlag der Wissenschaften, Berlin, 1959
EXAMPLE
1 * 13 = 13
14 * 13 = 182
24 * 13 = 312
178 * 13 = 2314
1095 * 13 = 14235
9642 * 13 = 125346
94975 * 13 = 1234675
949905 * 13 = 12348765
9496683 * 13 = 123456879
78727536 * 13 = 1023457968
CROSSREFS
Sequence in context: A009015 A067385 A097260 * A158548 A285399 A297581
KEYWORD
base,fini,full,nonn
AUTHOR
Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), May 24 2010, May 26 2010
STATUS
approved