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%I #12 Sep 26 2018 03:30:29
%S 13,182,312,2314,14235,125346,1234675,12348765,123456879,1023457968
%N Smallest multiple of 13 such that decimals digits 1, ..., k (k = 1, ..., 9) and 0 appear in any order.
%C 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:
%C 9th term: 123 456 879: (123 + 879) - 456 = 546, 546: 54 + (6 * 4) = 78 = 6 * 13.
%D Faith Javane, Zahlenmystik: Das Handbuch der Numerologie, Goldmann - Arkana, Frankfurt, 1995
%D Helmut Kracke, Mathe - musische Knobelisken. Tüfteleien für Tüftler und Laien, Dümmler, Bonn, 1982
%D Hugo Steinhaus, Kaleidoskop der Mathematik, Deutscher Verlag der Wissenschaften, Berlin, 1959
%e 1 * 13 = 13
%e 14 * 13 = 182
%e 24 * 13 = 312
%e 178 * 13 = 2314
%e 1095 * 13 = 14235
%e 9642 * 13 = 125346
%e 94975 * 13 = 1234675
%e 949905 * 13 = 12348765
%e 9496683 * 13 = 123456879
%e 78727536 * 13 = 1023457968
%Y Cf. A171768, A171744.
%K base,fini,full,nonn
%O 1,1
%A Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), May 24 2010, May 26 2010