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upside-down numbers
Numbers in which the sum of the i-th leftmost and i-th rightmost digits is 10 for each valid i. more

The first 600 upside-down numbers :
5, 19, 28, 37, 46, 55, 64, 73, 82, 91, 159, 258, 357, 456, 555, 654, 753, 852, 951, 1199, 1289, 1379, 1469, 1559, 1649, 1739, 1829, 1919, 2198, 2288, 2378, 2468, 2558, 2648, 2738, 2828, 2918, 3197, 3287, 3377, 3467, 3557, 3647, 3737, 3827, 3917, 4196, 4286, 4376, 4466, 4556, 4646, 4736, 4826, 4916, 5195, 5285, 5375, 5465, 5555, 5645, 5735, 5825, 5915, 6194, 6284, 6374, 6464, 6554, 6644, 6734, 6824, 6914, 7193, 7283, 7373, 7463, 7553, 7643, 7733, 7823, 7913, 8192, 8282, 8372, 8462, 8552, 8642, 8732, 8822, 8912, 9191, 9281, 9371, 9461, 9551, 9641, 9731, 9821, 9911, 11599, 12589, 13579, 14569, 15559, 16549, 17539, 18529, 19519, 21598, 22588, 23578, 24568, 25558, 26548, 27538, 28528, 29518, 31597, 32587, 33577, 34567, 35557, 36547, 37537, 38527, 39517, 41596, 42586, 43576, 44566, 45556, 46546, 47536, 48526, 49516, 51595, 52585, 53575, 54565, 55555, 56545, 57535, 58525, 59515, 61594, 62584, 63574, 64564, 65554, 66544, 67534, 68524, 69514, 71593, 72583, 73573, 74563, 75553, 76543, 77533, 78523, 79513, 81592, 82582, 83572, 84562, 85552, 86542, 87532, 88522, 89512, 91591, 92581, 93571, 94561, 95551, 96541, 97531, 98521, 99511, 111999, 112899, 113799, 114699, 115599, 116499, 117399, 118299, 119199, 121989, 122889, 123789, 124689, 125589, 126489, 127389, 128289, 129189, 131979, 132879, 133779, 134679, 135579, 136479, 137379, 138279, 139179, 141969, 142869, 143769, 144669, 145569, 146469, 147369, 148269, 149169, 151959, 152859, 153759, 154659, 155559, 156459, 157359, 158259, 159159, 161949, 162849, 163749, 164649, 165549, 166449, 167349, 168249, 169149, 171939, 172839, 173739, 174639, 175539, 176439, 177339, 178239, 179139, 181929, 182829, 183729, 184629, 185529, 186429, 187329, 188229, 189129, 191919, 192819, 193719, 194619, 195519, 196419, 197319, 198219, 199119, 211998, 212898, 213798, 214698, 215598, 216498, 217398, 218298, 219198, 221988, 222888, 223788, 224688, 225588, 226488, 227388, 228288, 229188, 231978, 232878, 233778, 234678, 235578, 236478, 237378, 238278, 239178, 241968, 242868, 243768, 244668, 245568, 246468, 247368, 248268, 249168, 251958, 252858, 253758, 254658, 255558, 256458, 257358, 258258, 259158, 261948, 262848, 263748, 264648, 265548, 266448, 267348, 268248, 269148, 271938, 272838, 273738, 274638, 275538, 276438, 277338, 278238, 279138, 281928, 282828, 283728, 284628, 285528, 286428, 287328, 288228, 289128, 291918, 292818, 293718, 294618, 295518, 296418, 297318, 298218, 299118, 311997, 312897, 313797, 314697, 315597, 316497, 317397, 318297, 319197, 321987, 322887, 323787, 324687, 325587, 326487, 327387, 328287, 329187, 331977, 332877, 333777, 334677, 335577, 336477, 337377, 338277, 339177, 341967, 342867, 343767, 344667, 345567, 346467, 347367, 348267, 349167, 351957, 352857, 353757, 354657, 355557, 356457, 357357, 358257, 359157, 361947, 362847, 363747, 364647, 365547, 366447, 367347, 368247, 369147, 371937, 372837, 373737, 374637, 375537, 376437, 377337, 378237, 379137, 381927, 382827, 383727, 384627, 385527, 386427, 387327, 388227, 389127, 391917, 392817, 393717, 394617, 395517, 396417, 397317, 398217, 399117, 411996, 412896, 413796, 414696, 415596, 416496, 417396, 418296, 419196, 421986, 422886, 423786, 424686, 425586, 426486, 427386, 428286, 429186, 431976, 432876, 433776, 434676, 435576, 436476, 437376, 438276, 439176, 441966, 442866, 443766, 444666, 445566, 446466, 447366, 448266, 449166, 451956, 452856, 453756, 454656, 455556, 456456, 457356, 458256, 459156, 461946, 462846, 463746, 464646, 465546, 466446, 467346, 468246, 469146, 471936, 472836, 473736, 474636, 475536, 476436, 477336, 478236, 479136, 481926, 482826, 483726, 484626, 485526, 486426, 487326, 488226, 489126, 491916, 492816, 493716, 494616, 495516, 496416, 497316, 498216, 499116, 511995, 512895, 513795, 514695, 515595, 516495, 517395, 518295, 519195, 521985, 522885, 523785, 524685, 525585, 526485, 527385, 528285, 529185, 531975, 532875, 533775, 534675, 535575, 536475, 537375, 538275, 539175, 541965, 542865, 543765, 544665, 545565, 546465, 547365, 548265, 549165, 551955, 552855, 553755, 554655, 555555, 556455, 557355, 558255, 559155, 561945, 562845, 563745, 564645, 565545, 566445, 567345, 568245, 569145, 571935, 572835, 573735, 574635, 575535, 576435, 577335, 578235, 579135, 581925, 582825, 583725, 584625, 585525, 586425, 587325, 588225, 589125, 591915, 592815, 593715, 594615, 595515, 596415, 597315, 598215, 599115, 611994, 612894, 613794, 614694, 615594, 616494, 617394, 618294, 619194, 621984, 622884, 623784, 624684, 625584.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 10761679 values, from 5 to 999999951111111).

n\r 0  1 
247829685978711 2 
353217094848669591301 3 
42391484292292523914843055786 4 
511957432391484239148423914842391484 5 
62365204269370526280029565052154964328501 6 
71537593153694715368781537264153720715381361537654 7 
811957421461462119574215205111195742146146311957421535275 8 
965615905853152247836986561590505314504783050729 9 
100119574211957421195742119574211957431195742119574211957421195742 10 
114892034891264891954891484891815870008489168489181489148489195489126

A pictorial representation of the table above
motab
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.