cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

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

Original entry on oeis.org

13, 182, 312, 2314, 14235, 125346, 1234675, 12348765, 123456879, 1023457968
Offset: 1

Views

Author

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

Keywords

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.

A173550 a(n) = k smallest exponent of N = 2^k of first prime(1) = 2 where string "p(1) ... p(n)" appears in the decimal representation of N (n=1,2,...).

Original entry on oeis.org

1, 41, 81, 256, 2810, 19680, 131516, 1812049
Offset: 1

Views

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Feb 21 2010

Keywords

Examples

			n=1: 2^1 = 2
n=2: 2^41 = 2199023255552, "23" appears on decimals 6-7
n=3: 2^81 = 2417851639229258349412352, "235" appears on decimals 22-24
n=4: 2^256 has 78 decimals, "2357" appears on decimals 20-23
2^256 = 115792089237316195423570985008687907853269984665640564039457584007913129639936

References

  • Julian Havil, Impossible?: Surprising Solutions to Counterintuitive Conundrums, Princeton University Press 2008

Crossrefs

Cf. A000079, A018802, A171132, A171242, A171489, A171652, A171768

Extensions

Extended and edited by Hans Havermann, Mar 20 2010
Showing 1-2 of 2 results.

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