A number n=x+y such that 1/x+1/y is just n divided by a power of 10. more
The first 600 sliding numbers :
2,
7,
11,
20,
25,
29,
52,
65,
70,
101,
110,
133,
200,
205,
250,
254,
290,
425,
502,
520,
641,
650,
700,
785,
925,
1001,
1010,
1100,
1258,
1330,
2000,
2005,
2050,
2225,
2500,
2504,
2540,
2900,
3157,
3445,
4025,
4250,
5002,
5020,
5200,
6266,
6325,
6410,
6500,
7000,
7850,
8125,
9250,
10001,
10010,
10100,
11000,
12508,
12580,
13300,
15689,
16265,
16625,
20000,
20005,
20050,
20500,
22025,
22250,
25000,
25004,
25040,
25400,
29000,
31282,
31570,
34450,
35125,
40025,
40250,
42500,
50002,
50020,
50200,
52000,
62516,
62660,
63250,
64100,
65000,
70000,
78253,
78500,
79405,
79625,
80125,
81250,
90925,
92500,
100001,
100010,
100100,
101000,
110000,
125008,
125080,
125800,
133000,
156314,
156890,
160625,
162650,
166250,
200000,
200005,
200050,
200500,
205000,
206125,
220250,
222500,
250000,
250004,
250040,
250400,
254000,
290000,
312532,
312820,
315700,
323125,
344500,
351250,
390881,
393185,
400025,
400250,
402500,
416225,
425000,
500002,
500020,
500200,
502000,
520000,
625016,
625160,
626600,
632500,
641000,
646625,
650000,
655625,
700000,
781378,
782530,
785000,
794050,
796250,
800125,
801250,
812500,
909250,
925000,
1000001,
1000010,
1000100,
1001000,
1010000,
1100000,
1250008,
1250080,
1250800,
1258000,
1330000,
1358125,
1562564,
1563140,
1568900,
1600625,
1606250,
1626500,
1662500,
1953637,
1958245,
2000000,
2000005,
2000050,
2000500,
2004325,
2005000,
2050000,
2061250,
2202500,
2225000,
2465125,
2500000,
2500004,
2500040,
2500400,
2504000,
2540000,
2900000,
2950625,
3125032,
3125320,
3128200,
3157000,
3203125,
3231250,
3445000,
3512500,
3906506,
3908810,
3931850,
4000025,
4000250,
4002500,
4025000,
4162250,
4250000,
5000002,
5000020,
5000200,
5002000,
5020000,
5200000,
6250016,
6250160,
6251600,
6266000,
6325000,
6410000,
6415625,
6466250,
6500000,
6556250,
7000000,
7073125,
7812628,
7813780,
7825300,
7850000,
7940500,
7962500,
8000125,
8001250,
8012500,
8125000,
9092500,
9250000,
9766649,
9775865,
9868025,
10000001,
10000010,
10000100,
10001000,
10010000,
10100000,
10789625,
11000000,
12500008,
12500080,
12500800,
12508000,
12580000,
12878125,
13300000,
13581250,
15625064,
15625640,
15631400,
15689000,
16000625,
16006250,
16062500,
16265000,
16625000,
19531762,
19536370,
19582450,
20000000,
20000005,
20000050,
20000500,
20005000,
20005625,
20043250,
20050000,
20500000,
20612500,
22025000,
22250000,
24651250,
25000000,
25000004,
25000040,
25000400,
25004000,
25040000,
25400000,
25990625,
29000000,
29506250,
31250032,
31250320,
31253200,
31282000,
31570000,
32003125,
32031250,
32312500,
34450000,
35125000,
39062756,
39065060,
39088100,
39318500,
40000025,
40000250,
40002500,
40025000,
40250000,
41622500,
42500000,
48830173,
48848605,
49032925,
50000002,
50000020,
50000200,
50002000,
50020000,
50200000,
50876125,
52000000,
53153125,
62500016,
62500160,
62501600,
62516000,
62660000,
63250000,
64015625,
64100000,
64156250,
64662500,
65000000,
65562500,
69308125,
70000000,
70731250,
78125128,
78126280,
78137800,
78253000,
78500000,
79405000,
79625000,
80000125,
80001250,
80012500,
80125000,
81250000,
90925000,
92500000,
97657274,
97666490,
97758650,
98680250,
100000001,
100000010,
100000100,
100001000,
100010000,
100100000,
101000000,
107896250,
110000000,
112165625,
125000008,
125000080,
125000800,
125008000,
125080000,
125800000,
128078125,
128781250,
133000000,
135812500,
156250064,
156250640,
156256400,
156314000,
156890000,
160000625,
160006250,
160062500,
160625000,
162650000,
166250000,
195313012,
195317620,
195363700,
195824500,
200000000,
200000005,
200000050,
200000500,
200005000,
200050000,
200056250,
200432500,
200500000,
205000000,
206125000,
220250000,
222500000,
244144721,
244181585,
244550225,
246512500,
248236625,
250000000,
250000004,
250000040,
250000400,
250004000,
250040000,
250400000,
253628125,
254000000,
256390625,
259906250,
285100625,
290000000,
295062500,
312500032,
312500320,
312503200,
312532000,
312820000,
315700000,
320003125,
320031250,
320312500,
323125000,
344500000,
351250000,
390625256,
390627560,
390650600,
390881000,
393185000,
400000025,
400000250,
400002500,
400025000,
400250000,
402500000,
416225000,
425000000,
488283298,
488301730,
488486050,
490329250,
500000002,
500000020,
500000200,
500002000,
500020000,
500200000,
502000000,
508761250,
513953125,
520000000,
531531250,
625000016,
625000160,
625001600,
625016000,
625160000,
626600000,
632500000,
640015625,
640156250,
641000000,
641562500,
646625000,
650000000,
653740625,
655625000,
693081250,
700000000,
707312500,
781250128,
781251280,
781262800,
781378000,
782530000,
785000000,
794050000,
796250000,
800000125,
800001250,
800012500,
800125000,
801250000,
812500000,
909250000,
925000000,
976563524,
976572740,
976664900,
977586500,
986802500,
1000000001,
1000000010,
1000000100,
1000001000,
1000010000,
1000100000,
1001000000,
1010000000,
1033765625,
1078962500,
1100000000,
1121656250,
1220711317,
1220785045,
1221522325,
1228895125,
1250000008,
1250000080,
1250000800,
1250008000,
1250080000,
1250800000,
1258000000,
1280078125,
1280781250,
1287812500,
1302623125,
1330000000,
1358125000,
1562500064,
1562500640,
1562506400,
1562564000,
1563140000,
1568900000,
1600000625,
1600006250,
1600062500,
1600625000,
1606250000,
1626500000,
1662500000,
1953125512,
1953130120,
1953176200,
1953637000,
1958245000,
2000000000,
2000000005,
2000000050,
2000000500,
2000005000,
2000050000,
2000500000,
2000562500,
2004325000,
2005000000,
2039903125,
2050000000,
2061250000,
2096828125,
2202500000,
2225000000,
2441410346,
2441447210,
2441815850,
2445502250,
2465125000,
2482366250,
2500000000,
2500000004,
2500000040,
2500000400,
2500004000,
2500040000,
2500400000,
2504000000,
2536281250,
2540000000,
2560390625,
2563906250,
2599062500,
2851006250.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 2271 values, from 2 to 986802500000000).
n\r | 0 | 1 |
2 | 2003 | 268 | 2 |
3 | 0 | 1127 | 1144 | 3 |
4 | 1733 | 266 | 270 | 2 | 4 |
5 | 2091 | 50 | 48 | 39 | 43 | 5 |
6 | 0 | 133 | 1009 | 0 | 994 | 135 | 6 |
7 | 381 | 311 | 316 | 317 | 314 | 319 | 313 | 7 |
8 | 1473 | 133 | 266 | 1 | 260 | 133 | 4 | 1 | 8 |
9 | 0 | 0 | 1144 | 0 | 0 | 0 | 0 | 1127 | 0 | 9 |
10 | 1858 | 19 | 42 | 5 | 38 | 233 | 31 | 6 | 34 | 5 | 10 |
11 | 229 | 228 | 128 | 240 | 431 | 0 | 0 | 465 | 215 | 110 | 225 |
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.