[seqfan] Re: square loop generalised to power loop

[hv at crypt.org]

Earlier I wrote:
:Neil Fernandez <primeness at borve.org> wrote:
::Another sequence is
::
::a(n):= smallest k such that {1, 2 ,..., k} can be arranged in a loop in
::which every consecutive pair sums to an nth power
::
::The sequence begins 1, 32, ...
:
:This seems to be the main one that's missing; I'll have a go at finding
:more terms for this in a week (when I return from a trip) - I think it
:should actually be easier than A304120.

First loop for cubes can be found at n=473, eg:
  353 376 136 207 9 334 395 117 226 286 443 69 56 456 273 239 104 408 321 191
  25 318 411 101 242 270 459 53 72 440 289 223 120 392 337 175 168 344 385 127
  216 296 433 79 46 466 263 249 94 418 311 32 184 328 401 111 232 280 449 63 1
  26 190 153 359 370 142 201 15 49 463 266 246 97 415 314 29 187 156 356 373
  139 204 12 331 398 114 229 283 446 66 59 453 276 236 107 405 324 19 8 208
  304 425 87 256 473 39 177 335 394 118 225 287 442 70 55 457 272 240 103 409
  320 23 193 150 362 367 145 198 18 325 404 108 235 277 452 60 65 447 282 230
  113 399 330 13 203 309 420 92 251 261 468 44 20 196 147 365 364 148 68 444
  285 227 116 396 333 10 17 326 403 109 234 278 451 61 3 213 299 430 82 134
  378 351 161 182 34 30 186 157 355 374 138 205 11 16 327 402 110 233 279 450
  62 2 6 210 302 427 85 131 381 348 164 179 37 27 316 413 99 244 268 461 51
  74 438 291 221 122 390 339 4 212 300 429 83 133 379 350 162 181 35 308 421
  91 252 260 469 43 173 170 342 387 125 218 294 435 77 48 464 265 247 96 416
  313 199 144 368 361 151 192 24 319 410 102 241 271 458 54 71 441 288 224
  119 393 336 7 209 303 426 86 130 382 347 165 178 38 305 424 88 255 257 472
  40 176 167 345 384 128 215 297 432 80 45 467 262 250 93 419 310 202 14 329
  400 112 231 281 448 64 152 360 369 143 200 312 417 95 248 264 465 47 78 434
  295 217 126 386 343 169 174 42 470 259 253 90 422 307 36 28 188 155 357 372
  140 76 436 293 219 124 388 341 171 172 340 389 123 220 292 437 75 141 371
  358 154 189 323 406 106 237 275 454 58 67 445 284 228 115 397 332 180 163
  349 380 132 211 301 428 84 41 471 258 254 89 423 306 206 137 375 354 158
  185 31 33 183 160 352 377 135 81 431 298 214 129 383 346 166 50 462 267 245
  98 414 315 197 146 366 363 149 194 22 5 338 391 121 222 290 439 73 52 460
  269 243 100 412 317 195 21 322 407 105 238 274 455 57 159

Looking for quads now.

Hugo