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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.

%I A378141 #11 Jan 17 2025 09:12:21
%S A378141 1,2,4,8,16,32,9,18,64,128,39,75,156,256,76,137,259
%N 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.
%C A378141 By necessity, all terms are distinct.
%C A378141 This sequence is finite; see A380112 for the infinite variant.
%H A378141 Rémy Sigrist, <a href="/A378141/a378141.gp.txt">PARI program</a>
%e A378141 The XOR difference triangle for the whole sequence is:
%e A378141                                     258
%e A378141                                   465 211
%e A378141                                 171 378 425
%e A378141                               367 452 190 279
%e A378141                             205 418 102 216 463
%e A378141                           163 110 460 426 370 189
%e A378141                          98 193 175 355 201 443 262
%e A378141                       195 161  96 207 428 357 222 472
%e A378141                      65 130  35  67 140 288  69 155 323
%e A378141                    36 101 231 196 135  11 299 366 501 182
%e A378141                  28  56  93 186 126 249 242 473 183 322 500
%e A378141                51  47  23  74 240 142 119 133 348 491 169 349
%e A378141              17  34  13  26  80 160  46  89 220 384 107 194 415
%e A378141            15  30  60  49  43 123 219 245 172 112 496 411 345 198
%e A378141          5   10  20  40  25  50  73 146 103 203 187 331 208 393 335
%e A378141        3   6   12  24  48  41  27  82 192 167 108 215 412 332 197 394
%e A378141      1   2   4   8   16  32  9   18  64 128  39  75 156 256  76 137 259
%o A378141 (PARI) \\ See Links section.
%Y A378141 Cf. A099884, A380112.
%K A378141 nonn,base,fini,full
%O A378141 1,2
%A A378141 _Rémy Sigrist_, Jan 09 2025