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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

%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

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Last modified December 1 07:48 EST 2023. Contains 367468 sequences. (Running on oeis4.)