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.

A337975 Multiplication table from A337946, read by antidiagonals.

Original entry on oeis.org

1, 3, 3, 7, 9, 7, 12, 21, 21, 12, 22, 36, 49, 36, 22, 30, 66, 84, 84, 66, 30, 47, 90, 154, 144, 154, 90, 47, 61, 141, 210, 264, 264, 210, 141, 61, 85, 183, 329, 360, 484, 360, 329, 183, 85, 113, 255, 427, 564, 660, 660, 564, 427, 255, 113, 126, 339, 595, 732, 1034, 900, 1034, 732, 595, 339, 126
Offset: 1

Views

Author

Peter Kagey, Oct 05 2020

Keywords

Examples

			Multiplication table for A337946 begins:
  *  |  1   3   7   12   22   30   47   61   85
-----+-----------------------------------------
   1 |  1   3   7   12   22   30   47   61   85
   3 |  3   9  21   36   66   90  141  183  255
   7 |  7  21  49   84  154  210  329  427  595
  12 | 12  36  84  144  264  360  564  732 1020
  22 | 22  66 154  264  484  660 1034 1342 1870
  30 | 30  90 210  360  660  900 1410 1830 2550
  47 | 47 141 329  564 1034 1410 2209 2867 3995
  61 | 61 183 427  732 1342 1830 2867 3721 5185
  85 | 85 255 595 1020 1870 2550 3995 5185 7225

Links

Crossrefs

Cf. A337662, A337946, A338017, A338034.
Cf. A337973 (addition), A337974 (read by rows).

A338034 Multiplication table of A337656, read by antidiagonals.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 7, 9, 7, 0, 0, 12, 21, 21, 12, 0, 0, 20, 36, 49, 36, 20, 0, 0, 30, 60, 84, 84, 60, 30, 0, 0, 44, 90, 140, 144, 140, 90, 44, 0, 0, 65, 132, 210, 240, 240, 210, 132, 65, 0, 0, 91, 195, 308, 360, 400, 360, 308, 195, 91, 0
Offset: 1

Views

Author

Peter Kagey, Oct 07 2020

Keywords

Examples

			Multiplication table begins:
   * | 0  1   3   7  12   20   30   44   65
-----+-------------------------------------
   0 | 0  0   0   0   0    0    0    0    0
   1 | 0  1   3   7  12   20   30   44   65
   3 | 0  3   9  21  36   60   90  132  195
   7 | 0  7  21  49  84  140  210  308  455
  12 | 0 12  36  84 144  240  360  528  780
  20 | 0 20  60 140 240  400  600  880 1300
  30 | 0 30  90 210 360  600  900 1320 1950
  44 | 0 44 132 308 528  880 1320 1936 2860
  65 | 0 65 195 455 780 1300 1950 2860 4225

Links

Crossrefs

Cf. A337656, A337657, A338032 (addition table), A338033 (by rows).
Cf. A337662, A337975, A338017.
Showing 1-5 of 5 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.