A338012 -id:A338012 - cp's OEIS frontend

A338014 Triangular array read by rows: T(n,k) = A338012(n) + A338012(k) for 1 <= k <= n.

0, 3, 6, 4, 7, 8, 10, 13, 14, 20, 18, 21, 22, 28, 36, 23, 26, 27, 33, 41, 46, 34, 37, 38, 44, 52, 57, 68, 55, 58, 59, 65, 73, 78, 89, 110, 67, 70, 71, 77, 85, 90, 101, 122, 134, 93, 96, 97, 103, 111, 116, 127, 148, 160, 186, 95, 98, 99, 105, 113, 118, 129, 150, 162, 188, 190

Offset: 1

Peter Kagey, Oct 06 2020

			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

Peter Kagey, Table of n, a(n) for n = 1..10011 (first 141 rows, flattened)

Cf. A338012, A338015 (by antidiagonals), A338016 (multiplication).

Cf. A337659, A337972.

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

Peter Kagey, Oct 06 2020

			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

Peter Kagey, Table of n, a(n) for n = 1..10011 (first 141 antidiagonals, flattened)

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

Peter Kagey, Oct 06 2020

			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

Peter Kagey, Table of n, a(n) for n = 1..10011 (first 141 rows, flattened)

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

Cf. A337661, A337974.

A338017 Multiplication table of A338012, read by antidiagonals.

Original entry on oeis.org

0, 0, 0, 0, 9, 0, 0, 12, 12, 0, 0, 30, 16, 30, 0, 0, 54, 40, 40, 54, 0, 0, 69, 72, 100, 72, 69, 0, 0, 102, 92, 180, 180, 92, 102, 0, 0, 165, 136, 230, 324, 230, 136, 165, 0, 0, 201, 220, 340, 414, 414, 340, 220, 201, 0, 0, 279, 268, 550, 612, 529, 612, 550, 268, 279, 0

Offset: 1

Peter Kagey, Oct 06 2020

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

Peter Kagey, Table of n, a(n) for n = 1..10011 (first 141 antidiagonals, flattened)

Cf. A338012, A338015 (addition table), A338016 (by rows).

Cf. A337662, A337975.

A338013 The list of positive integers that do not appear in the addition or multiplication tables of A338012.

Original entry on oeis.org

1, 2, 5, 11, 15, 17, 19, 24, 25, 29, 31, 32, 35, 39, 42, 43, 45, 47, 48, 49, 50, 51, 53, 56, 60, 61, 62, 63, 64, 66, 74, 75, 76, 79, 80, 81, 82, 83, 84, 86, 87, 88, 91, 94, 104, 106, 107, 108, 109, 112, 114, 115, 117, 119, 121, 125, 126, 128, 131, 132, 133

Offset: 1

Peter Kagey, Oct 06 2020

nonn

			The first four terms of this sequence are 1, 2, 5, and 11 because these are the four smallest positive integers that do not appear in the addition and multiplication tables of A338012.
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

Peter Kagey, Table of n, a(n) for n = 1..10000
Peter Kagey, Haskell Program.

Cf. A338012.

Cf. A337657, A337658, A337947.

cp's OEIS Frontend

A338014 Triangular array read by rows: T(n,k) = A338012(n) + A338012(k) for 1 <= k <= n.

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A338015 Addition table of A338012, read by antidiagonals.

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

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A338017 Multiplication table of A338012, read by antidiagonals.

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A338013 The list of positive integers that do not appear in the addition or multiplication tables of A338012.

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