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 1-3 of 3 results.

A062891 When expressed in base 3 and then interpreted in base 9, is a multiple of the original number.

Original entry on oeis.org

0, 1, 2, 3, 6, 9, 13, 18, 26, 27, 34, 39, 47, 54, 78, 81, 91, 102, 117, 121, 141, 162, 182, 234, 242, 243, 262, 273, 306, 351, 363, 423, 486, 546, 702, 726, 729, 757, 786, 819, 918, 1048, 1053, 1089, 1093, 1183, 1269, 1458, 1514, 1638, 2106, 2178, 2186, 2187
Offset: 1

Views

Author

Erich Friedman, Jul 21 2001

Keywords

Examples

			13 in base 3 is 111, which interpreted in base 9 is 91 = 7*13.

Links

Crossrefs

Cf. A007089 (base 3), A007095 (base 9), A037314 (base 3 -> 9).
Other digit spreads: A062846 (binary), A343550 (decimal).

Programs

  • Maple
    q:= n-> (l-> n=0 or 0=irem(add(l[i]*9^(i-1),
         i=1..nops(l)), n))(convert(n, base, 3)):
select(q, [$0..3000])[];  # Alois P. Heinz, Apr 20 2021
  • Mathematica
    Join[{0},Select[Range[2200],Divisible[FromDigits[IntegerDigits[#,3],9],#]&]] (* Harvey P. Dale, Apr 11 2017 *)

Extensions

Offset changed to 1 by Kevin Ryde, Apr 24 2021

A343551 Numbers m/k where the number m is formed by inserting a digit 0 between each pair of digits in k, and m is divisible by k.

Original entry on oeis.org

10, 7, 6, 10, 10, 10, 9, 10, 10, 10, 10, 10, 100, 91, 85, 81, 70, 60, 100, 91, 85, 82, 73, 100, 91, 85, 100, 91, 90, 85, 100, 91, 100, 91, 100, 94, 91, 100, 91, 100, 91, 1000, 961, 910, 853, 850, 810, 739, 721, 700, 676, 637, 600, 571, 546, 1000, 961, 91
Offset: 1

Views

Author

Lars Blomberg, Apr 19 2021

Keywords

Comments

This sequence is parallel to A343550 and A343552, therefore some values are repeated.

Examples

			6 is a term because 108/18=6, and so is 853 because 1010805/1185=853.
10101/111=91, 1010100/1110=910, 101010000/11100=9100, etc. are all terms.
1000401/1041=961 and 2000802/2082=961 are terms but not 3123.

Crossrefs

Cf. A051022, A285176, A343550, A343552.

A343552 Numbers m such that for some number k dividing n, m is formed by inserting a digit 0 between each pair of digits of k.

Original entry on oeis.org

100, 105, 108, 200, 300, 400, 405, 500, 600, 700, 800, 900, 10000, 10101, 10200, 10206, 10500, 10800, 20000, 20202, 20400, 20500, 20805, 30000, 30303, 30600, 40000, 40404, 40500, 40800, 50000, 50505, 60000, 60606, 70000, 70500, 70707, 80000, 80808, 90000
Offset: 1

Views

Author

Lars Blomberg, Apr 19 2021

Keywords

Comments

If m is a term then so is m*10^(2i), i > 0.
If m is a term then so is m*i, 2 <= i <= 9 as long as no carry occurs in the multiplication.

Examples

			108 is a term because 108/18=6, and so is 1010805 because 1010805/1185=853.

Crossrefs

Cf. A051022, A285176, A343550, A343551.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.