A380112 -id:A380112 - cp's OEIS frontend

A380148 Triangle T(n, k), n > 0, k = 1..n, read by rows; T(n, 1) = A380112(n), and for any k in 2..n, T(n, k) = T(n, k-1) XOR T(n-1, k-1) (where XOR denotes the bitwise XOR operator).

1, 2, 3, 4, 6, 5, 8, 12, 10, 15, 16, 24, 20, 30, 17, 32, 48, 40, 60, 34, 51, 9, 41, 25, 49, 13, 47, 28, 18, 27, 50, 43, 26, 23, 56, 36, 64, 82, 73, 123, 80, 74, 93, 101, 65, 128, 192, 146, 219, 160, 240, 186, 231, 130, 195, 39, 167, 103, 245, 46, 142, 126, 196, 35, 161, 98

Offset: 1

Rémy Sigrist, Jan 13 2025

This sequence corresponds to the XOR difference triangle associated with A380112. All terms are distinct.

			Triangle T(n, k) begins:
                        1
                      2   3
                    4   6   5
                  8   12  10  15
                16  24  20  30  17
              32  48  40  60  34  51
            9   41  25  49  13  47  28
          18  27  50  43  26  23  56  36
        64  82  73 123  80  74  93 101  65
     128 192 146 219 160 240 186 231 130 195

Rémy Sigrist, PARI program

Cf. A099884, A380112.

PARI
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\\ See Links section.
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A378141 For any n > 0, a(n) is the least positive integer such that the XOR difference triangle with bottom row (a(1), ..., a(n)) has distinct values.

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 9, 18, 64, 128, 39, 75, 156, 256, 76, 137, 259

Offset: 1

Rémy Sigrist, Jan 09 2025

By necessity, all terms are distinct.

This sequence is finite; see A380112 for the infinite variant.

			The XOR difference triangle for the whole sequence is:
                                    258
                                  465 211
                                171 378 425
                              367 452 190 279
                            205 418 102 216 463
                          163 110 460 426 370 189
                         98 193 175 355 201 443 262
                      195 161  96 207 428 357 222 472
                     65 130  35  67 140 288  69 155 323
                   36 101 231 196 135  11 299 366 501 182
                 28  56  93 186 126 249 242 473 183 322 500
               51  47  23  74 240 142 119 133 348 491 169 349
             17  34  13  26  80 160  46  89 220 384 107 194 415
           15  30  60  49  43 123 219 245 172 112 496 411 345 198
         5   10  20  40  25  50  73 146 103 203 187 331 208 393 335
       3   6   12  24  48  41  27  82 192 167 108 215 412 332 197 394
     1   2   4   8   16  32  9   18  64 128  39  75 156 256  76 137 259

Rémy Sigrist, PARI program

Cf. A099884, A380112.

PARI
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\\ See Links section.
```

cp's OEIS Frontend

A380148 Triangle T(n, k), n > 0, k = 1..n, read by rows; T(n, 1) = A380112(n), and for any k in 2..n, T(n, k) = T(n, k-1) XOR T(n-1, k-1) (where XOR denotes the bitwise XOR operator).

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