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.

A343045 a(0) = 0 and for any n > 0, a(n) = A343044(a(n-1), n).

Original entry on oeis.org

0, 1, 3, 3, 5, 5, 11, 11, 11, 11, 11, 11, 17, 17, 17, 17, 17, 17, 23, 23, 23, 23, 23, 23, 29, 29, 29, 29, 29, 29, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 89, 89, 89, 89, 89, 89, 89
Offset: 0

Views

Author

Rémy Sigrist, Apr 05 2021

Keywords

Comments

This sequence has similarities with A087052 and A343041.
If we remove duplicate terms, then we obtain A343048.

Examples

			The first terms, in decimal and in primorial base, are:
  n   a(n)  prim(n)  prim(a(n))
  --  ----  -------  ----------
   0     0        0           0
   1     1        1           1
   2     3       10          11
   3     3       11          11
   4     5       20          21
   5     5       21          21
   6    11      100         121
   7    11      101         121
   8    11      110         121
   9    11      111         121
  10    11      120         121
  11    11      121         121
  12    17      200         221
  13    17      201         221
  14    17      210         221

Links

Crossrefs

Cf. A343041, A343044, A343048.
Cf. A087052.

Programs

  • PARI
    See Links section.

A343040 Array T(n, k), n, k >= 0, read by antidiagonals; lunar addition table for the factorial base.

Original entry on oeis.org

0, 1, 1, 2, 1, 2, 3, 3, 3, 3, 4, 3, 2, 3, 4, 5, 5, 3, 3, 5, 5, 6, 5, 4, 3, 4, 5, 6, 7, 7, 5, 5, 5, 5, 7, 7, 8, 7, 8, 5, 4, 5, 8, 7, 8, 9, 9, 9, 9, 5, 5, 9, 9, 9, 9, 10, 9, 8, 9, 10, 5, 10, 9, 8, 9, 10, 11, 11, 9, 9, 11, 11, 11, 11, 9, 9, 11, 11, 12, 11, 10, 9, 10, 11, 6, 11, 10, 9, 10, 11, 12
Offset: 0

Views

Author

Rémy Sigrist, Apr 03 2021

Keywords

Comments

The i-th digit of T(n, k) in factorial base is the largest of the i-th digits of n and of k in factorial base.
For n = 0..23, the factorial and primorial base representations of n are the same; hence the date sections for this sequence and for A343044 are the same.

Examples

			Array T(n, k) begins:
  n\k|   0   1   2   3   4   5   6   7   8   9  10  11  12
  ---+----------------------------------------------------
    0|   0   1   2   3   4   5   6   7   8   9  10  11  12
    1|   1   1   3   3   5   5   7   7   9   9  11  11  13
    2|   2   3   2   3   4   5   8   9   8   9  10  11  14
    3|   3   3   3   3   5   5   9   9   9   9  11  11  15
    4|   4   5   4   5   4   5  10  11  10  11  10  11  16
    5|   5   5   5   5   5   5  11  11  11  11  11  11  17
    6|   6   7   8   9  10  11   6   7   8   9  10  11  12
    7|   7   7   9   9  11  11   7   7   9   9  11  11  13
    8|   8   9   8   9  10  11   8   9   8   9  10  11  14
    9|   9   9   9   9  11  11   9   9   9   9  11  11  15
   10|  10  11  10  11  10  11  10  11  10  11  10  11  16
   11|  11  11  11  11  11  11  11  11  11  11  11  11  17
   12|  12  13  14  15  16  17  12  13  14  15  16  17  12
Array T(n, k) begins in factorial base:
  n\k|    0    1   10   11   20   21  100  101  110  111  120  121  200
  ---+-----------------------------------------------------------------
    0|    0    1   10   11   20   21  100  101  110  111  120  121  200
    1|    1    1   11   11   21   21  101  101  111  111  121  121  201
   10|   10   11   10   11   20   21  110  111  110  111  120  121  210
   11|   11   11   11   11   21   21  111  111  111  111  121  121  211
   20|   20   21   20   21   20   21  120  121  120  121  120  121  220
   21|   21   21   21   21   21   21  121  121  121  121  121  121  221
  100|  100  101  110  111  120  121  100  101  110  111  120  121  200
  101|  101  101  111  111  121  121  101  101  111  111  121  121  201
  110|  110  111  110  111  120  121  110  111  110  111  120  121  210
  111|  111  111  111  111  121  121  111  111  111  111  121  121  211
  120|  120  121  120  121  120  121  120  121  120  121  120  121  220
  121|  121  121  121  121  121  121  121  121  121  121  121  121  221
  200|  200  201  210  211  220  221  200  201  210  211  220  221  200

Links

Crossrefs

Cf. A087061, A108731, A343040, A343044.

Programs

  • PARI
    T(n,k) = { my (v=0, f=1); for (r=2, oo, if (n==0 && k==0, return (v), v+=max(n%r, k%r)*f; f*=r; n\=r; k\=r)) }

Formula

T(n, k) = T(k, n).
T(m, T(n, k)) = T(T(m, n), k).
T(n, 0) = n.
T(n, n) = n.

A343046 Array T(n, k), n, k >= 0, read by antidiagonals; lunar multiplication table for the primorial 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, 30, 9, 12, 9, 30, 7, 0, 0, 8, 32, 36, 14, 14, 36, 32, 8, 0, 0, 9, 36, 39, 30, 15, 30, 39, 36, 9, 0, 0, 8, 38, 38, 32, 36, 36, 32, 38, 38, 8, 0
Offset: 0

Views

Author

Rémy Sigrist, Apr 05 2021

Keywords

Comments

To compute T(n, k):
- write the primorial 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(9, 10):
9 -> 1 1 1
10 -> x 1 2 0
-------
0 0 0
1 1 1
+ 1 1 1
-----------
1 1 1 1 0 -> 248 = T(9, 10)
See A343044 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  ->  A328841
    2|  0  2   6   8   6   8   30   32   36   38   36   38   30
    3|  0  3   8   9   8   9   36   39   38   39   38   39   36
    4|  0  2   6   8  12  14   30   32   36   38   42   44   60
    5|  0  3   8   9  14  15   36   39   38   39   44   45   66
    6|  0  6  30  36  30  36  210  216  240  246  240  246  210
    7|  0  7  32  39  32  39  216  217  248  249  248  249  216
    8|  0  8  36  38  36  38  240  248  246  248  246  248  240
    9|  0  9  38  39  38  39  246  249  248  249  248  249  246
   10|  0  8  36  38  42  44  240  248  246  248  252  254  270
   11|  0  9  38  39  44  45  246  249  248  249  254  255  276
   12|  0  6  30  36  60  66  210  216  240  246  270  276  420

Links

Crossrefs

Cf. A087062, A235168, A328841, A343042, A343044, A343047.

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.
T(n, 1) = A328841(n).
T(n, n) = A343047(n).
Showing 1-3 of 3 results.

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

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