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.

A343047 a(n) = A343046(n, n).

Original entry on oeis.org

0, 1, 6, 9, 12, 15, 210, 217, 246, 249, 252, 255, 420, 427, 456, 459, 492, 495, 630, 637, 666, 669, 702, 705, 840, 847, 876, 879, 912, 915, 30030, 30061, 30246, 30279, 30252, 30285, 32550, 32587, 32586, 32589, 32592, 32595, 32760, 32797, 32796, 32799, 32832
Offset: 0

Views

Author

Rémy Sigrist, Apr 05 2021

Keywords

Comments

This sequence has similarities with A087019 and A343043.

Examples

			For n = 2:
- the primorial base representation of 2 is "10", so:
         1 0
       x 1 0
       -----
         0 0
     + 1 0
     -------
       1 0 0
- hence a(2) = 2*3 = 6.

Links

Crossrefs

Cf. A002110, A143293, A343046.
Cf. A087019, A343043.

Programs

  • PARI
    See Links section.

Formula

a(A002110(k)) = A002110(2*k) for any k >= 0.
a(A143293(k)) = A143293(2*k) for any k >= 0.

A343042 Array T(n, k), n, k >= 0, read by antidiagonals; lunar multiplication table for the factorial base.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 6, 3, 0, 0, 2, 8, 8, 2, 0, 0, 3, 6, 9, 6, 3, 0, 0, 6, 8, 8, 8, 8, 6, 0, 0, 7, 24, 9, 12, 9, 24, 7, 0, 0, 8, 26, 30, 14, 14, 30, 26, 8, 0, 0, 9, 30, 33, 24, 15, 24, 33, 30, 9, 0, 0, 8, 32, 32, 26, 30, 30, 26, 32, 32, 8, 0
Offset: 0

Views

Author

Rémy Sigrist, Apr 05 2021

Keywords

Comments

To compute T(n, k):
- write the factorial base representations of n and of k on two lines, right aligned,
- to "multiply" two digits: take the smallest,
- to "add" two digits: take the largest,
- for example, for T(13, 14):
12 -> 2 0 1
14 -> x 2 1 0
-------
0 0 0
1 0 1
+ 2 0 1
-----------
2 1 1 1 0 -> 272 = T(13, 14)
See A343040 for the corresponding addition table.

Examples

			Array T(n, k) begins:
  n\k|  0  1   2   3   4   5    6    7    8    9   10   11   12
  ---+---------------------------------------------------------
    0|  0  0   0   0   0   0    0    0    0    0    0    0    0
    1|  0  1   2   3   2   3    6    7    8    9    8    9    6
    2|  0  2   6   8   6   8   24   26   30   32   30   32   24
    3|  0  3   8   9   8   9   30   33   32   33   32   33   30
    4|  0  2   6   8  12  14   24   26   30   32   36   38   48
    5|  0  3   8   9  14  15   30   33   32   33   38   39   54
    6|  0  6  24  30  24  30  120  126  144  150  144  150  120
    7|  0  7  26  33  26  33  126  127  152  153  152  153  126
    8|  0  8  30  32  30  32  144  152  150  152  150  152  144
    9|  0  9  32  33  32  33  150  153  152  153  152  153  150
   10|  0  8  30  32  36  38  144  152  150  152  156  158  168
   11|  0  9  32  33  38  39  150  153  152  153  158  159  174
   12|  0  6  24  30  48  54  120  126  144  150  168  174  240

Links

Crossrefs

Cf. A087062, A343040, A343046.

Programs

  • PARI
    See Links section.

Formula

T(n, k) = T(k, n).
T(m, T(n, k)) = T(T(m, n), k).
T(n, 0) = 0.
Showing 1-2 of 2 results.

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

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