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 |
2 | 4782968 | 5978711 | 2 |
3 | 5321709 | 4848669 | 591301 | 3 |
4 | 2391484 | 2922925 | 2391484 | 3055786 | 4 |
5 | 1195743 | 2391484 | 2391484 | 2391484 | 2391484 | 5 |
6 | 2365204 | 2693705 | 262800 | 2956505 | 2154964 | 328501 | 6 |
7 | 1537593 | 1536947 | 1536878 | 1537264 | 1537207 | 1538136 | 1537654 | 7 |
8 | 1195742 | 1461462 | 1195742 | 1520511 | 1195742 | 1461463 | 1195742 | 1535275 | 8 |
9 | 6561 | 59058 | 531522 | 4783698 | 6561 | 59050 | 531450 | 4783050 | 729 | 9 |
10 | 0 | 1195742 | 1195742 | 1195742 | 1195742 | 1195743 | 1195742 | 1195742 | 1195742 | 1195742 | 10 |
11 | 489203 | 489126 | 489195 | 489148 | 489181 | 5870008 | 489168 | 489181 | 489148 | 489195 | 489126 |
A pictorial representation of the table above
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.