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 1-5 of 5 results.

A338012 a(1)=0; thereafter, a(n) is the smallest number such that the addition and multiplication tables for (a(1),...,a(n)) together contain n^2 different entries (the maximum possible).

Original entry on oeis.org

0, 3, 4, 10, 18, 23, 34, 55, 67, 93, 95, 120, 149, 166, 228, 271, 351, 398, 439, 505, 563, 611, 732, 771, 806, 924, 1052, 1121, 1278, 1412, 1586, 1654, 1875, 2012, 2245, 2341, 2445, 2616, 2819, 2920, 3034, 3322, 3518, 3754, 3918, 4016, 4311, 4649, 4848, 5321
Offset: 1

Views

Author

Peter Kagey, Oct 06 2020

Keywords

Examples

			Addition table begins:
   + |  0  3  4 10 18 23  34  55  67
-----+-------------------------------
   0 |  0
   3 |  3  6
   4 |  4  7  8
  10 | 10 13 14 20
  18 | 18 21 22 28 36
  23 | 23 26 27 33 41 46
  34 | 34 37 38 44 52 57  68
  55 | 55 58 59 65 73 78  89 110
  67 | 67 70 71 77 85 90 101 122 134
Multiplication table begins:
   * | 0   3   4  10   18   23   34   55   67
-----+---------------------------------------
   0 | 0
   3 | 0   9
   4 | 0  12  16
  10 | 0  30  40 100
  18 | 0  54  72 180  324
  23 | 0  69  92 230  414  529
  34 | 0 102 136 340  612  782 1156
  55 | 0 165 220 550  990 1265 1870 3025
  67 | 0 201 268 670 1206 1541 2278 3685 4489

Links

Crossrefs

Cf. A337655, A337656, A337946.
Cf. A338013, A338014, A338015, A338016, A338017.

A338015 Addition table of A338012, read by antidiagonals.

Original entry on oeis.org

0, 3, 3, 4, 6, 4, 10, 7, 7, 10, 18, 13, 8, 13, 18, 23, 21, 14, 14, 21, 23, 34, 26, 22, 20, 22, 26, 34, 55, 37, 27, 28, 28, 27, 37, 55, 67, 58, 38, 33, 36, 33, 38, 58, 67, 93, 70, 59, 44, 41, 41, 44, 59, 70, 93, 95, 96, 71, 65, 52, 46, 52, 65, 71, 96, 95
Offset: 1

Views

Author

Peter Kagey, Oct 06 2020

Keywords

Examples

			Addition table begins:
   + |  0  3  4 10 18 23  34  55  67
-----+-------------------------------
   0 |  0  3  4 10 18 23  34  55  67
   3 |  3  6  7 13 21 26  37  58  70
   4 |  4  7  8 14 22 27  38  59  71
  10 | 10 13 14 20 28 33  44  65  77
  18 | 18 21 22 28 36 41  52  73  85
  23 | 23 26 27 33 41 46  57  78  90
  34 | 34 37 38 44 52 57  68  89 101
  55 | 55 58 59 65 73 78  89 110 122
  67 | 67 70 71 77 85 90 101 122 134

Links

Crossrefs

Cf. A338012, A338014 (by rows), A338017 (multiplication table).
Cf. A337660, A337973.

A338016 Triangular array read by rows: T(n,k) = A338012(n) * A338012(k) for 1 <= k <= n.

Original entry on oeis.org

0, 0, 9, 0, 12, 16, 0, 30, 40, 100, 0, 54, 72, 180, 324, 0, 69, 92, 230, 414, 529, 0, 102, 136, 340, 612, 782, 1156, 0, 165, 220, 550, 990, 1265, 1870, 3025, 0, 201, 268, 670, 1206, 1541, 2278, 3685, 4489, 0, 279, 372, 930, 1674, 2139, 3162, 5115, 6231, 8649
Offset: 1

Views

Author

Peter Kagey, Oct 06 2020

Keywords

Examples

			Multiplication table begins:
   * | 0   3   4  10   18   23   34   55   67
-----+---------------------------------------
   0 | 0
   3 | 0   9
   4 | 0  12  16
  10 | 0  30  40 100
  18 | 0  54  72 180  324
  23 | 0  69  92 230  414  529
  34 | 0 102 136 340  612  782 1156
  55 | 0 165 220 550  990 1265 1870 3025
  67 | 0 201 268 670 1206 1541 2278 3685 4489

Links

Crossrefs

Cf. A338012, A338014 (addition), A338017 (by antidiagonals).
Cf. A337661, A337974.

A337972 Triangular array read by rows: T(n,k) = A337946(n) + A337946(k), for 1 <= k <= n.

Original entry on oeis.org

2, 4, 6, 8, 10, 14, 13, 15, 19, 24, 23, 25, 29, 34, 44, 31, 33, 37, 42, 52, 60, 48, 50, 54, 59, 69, 77, 94, 62, 64, 68, 73, 83, 91, 108, 122, 86, 88, 92, 97, 107, 115, 132, 146, 170, 114, 116, 120, 125, 135, 143, 160, 174, 198, 226, 127, 129, 133, 138, 148, 156, 173, 187, 211, 239, 252
Offset: 1

Views

Author

Peter Kagey, Oct 05 2020

Keywords

Comments

This sequence, A337947, and A337974 partition the positive integers.

Examples

			Addition table for A337946 begins:
  +  |  1  3  7 12  22  30  47  61  85
-----+--------------------------------
   1 |  2
   3 |  4  6
   7 |  8 10 14
  12 | 13 15 19 24
  22 | 23 25 29 34  44
  30 | 31 33 37 42  52  60
  47 | 48 50 54 59  69  77  94
  61 | 62 64 68 73  83  91 108 122
  85 | 86 88 92 97 107 115 132 146 170

Links

Crossrefs

Cf. A337659, A337946, A338014, A338031.
Cf. A337973 (read by antidiagonals), A337974 (multiplication table).

A338031 Triangular array read by rows: T(n,k) = A337656(n) + A337656(k) for 1 <= k <= n.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 8, 10, 14, 12, 13, 15, 19, 24, 20, 21, 23, 27, 32, 40, 30, 31, 33, 37, 42, 50, 60, 44, 45, 47, 51, 56, 64, 74, 88, 65, 66, 68, 72, 77, 85, 95, 109, 130, 91, 92, 94, 98, 103, 111, 121, 135, 156, 182, 107, 108, 110, 114, 119, 127, 137, 151, 172, 198, 214
Offset: 1

Views

Author

Peter Kagey, Oct 07 2020

Keywords

Examples

			Addition table begins:
   + |  0  1  3  7 12 20 30  44  65
-----+-----------------------------
   0 |  0
   1 |  1  2
   3 |  3  4  6
   7 |  7  8 10 14
  12 | 12 13 15 19 24
  20 | 20 21 23 27 32 40
  30 | 30 31 33 37 42 50 60
  44 | 44 45 47 51 56 64 74  88
  65 | 65 66 68 72 77 85 95 109 130

Links

Crossrefs

Cf. A337656, A337657, A338032 (by antidiagonals), A338033 (multiplication).
Cf. A337659, A337972, A338014.
Showing 1-5 of 5 results.

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