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A178303
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Smallest multiple of 13 such that decimals digits 1, ..., k (k = 1, ..., 9) and 0 appear in any order.
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3
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OFFSET
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1,1
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COMMENTS
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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.
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REFERENCES
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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
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LINKS
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EXAMPLE
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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
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CROSSREFS
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KEYWORD
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base,fini,full,nonn
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AUTHOR
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Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), May 24 2010, May 26 2010
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STATUS
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approved
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