A178303 Smallest multiple of 13 such that decimals digits 1, ..., k (k = 1, ..., 9) and 0 appear in any order.

13, 182, 312, 2314, 14235, 125346, 1234675, 12348765, 123456879, 1023457968

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), May 24 2010, May 26 2010

Keywords

• base
• fini
• full
• nonn

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.

Examples

			         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
		

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

Crossrefs

Cf. A171768, A171744.