A number that remains the same when read upside down. more
The first 600 strobogrammatic numbers :
1,
8,
11,
69,
88,
96,
101,
111,
181,
609,
619,
689,
808,
818,
888,
906,
916,
986,
1001,
1111,
1691,
1881,
1961,
6009,
6119,
6699,
6889,
6969,
8008,
8118,
8698,
8888,
8968,
9006,
9116,
9696,
9886,
9966,
10001,
10101,
10801,
11011,
11111,
11811,
16091,
16191,
16891,
18081,
18181,
18881,
19061,
19161,
19861,
60009,
60109,
60809,
61019,
61119,
61819,
66099,
66199,
66899,
68089,
68189,
68889,
69069,
69169,
69869,
80008,
80108,
80808,
81018,
81118,
81818,
86098,
86198,
86898,
88088,
88188,
88888,
89068,
89168,
89868,
90006,
90106,
90806,
91016,
91116,
91816,
96096,
96196,
96896,
98086,
98186,
98886,
99066,
99166,
99866,
100001,
101101,
106901,
108801,
109601,
110011,
111111,
116911,
118811,
119611,
160091,
161191,
166991,
168891,
169691,
180081,
181181,
186981,
188881,
189681,
190061,
191161,
196961,
198861,
199661,
600009,
601109,
606909,
608809,
609609,
610019,
611119,
616919,
618819,
619619,
660099,
661199,
666999,
668899,
669699,
680089,
681189,
686989,
688889,
689689,
690069,
691169,
696969,
698869,
699669,
800008,
801108,
806908,
808808,
809608,
810018,
811118,
816918,
818818,
819618,
860098,
861198,
866998,
868898,
869698,
880088,
881188,
886988,
888888,
889688,
890068,
891168,
896968,
898868,
899668,
900006,
901106,
906906,
908806,
909606,
910016,
911116,
916916,
918816,
919616,
960096,
961196,
966996,
968896,
969696,
980086,
981186,
986986,
988886,
989686,
990066,
991166,
996966,
998866,
999666,
1000001,
1001001,
1008001,
1010101,
1011101,
1018101,
1060901,
1061901,
1068901,
1080801,
1081801,
1088801,
1090601,
1091601,
1098601,
1100011,
1101011,
1108011,
1110111,
1111111,
1118111,
1160911,
1161911,
1168911,
1180811,
1181811,
1188811,
1190611,
1191611,
1198611,
1600091,
1601091,
1608091,
1610191,
1611191,
1618191,
1660991,
1661991,
1668991,
1680891,
1681891,
1688891,
1690691,
1691691,
1698691,
1800081,
1801081,
1808081,
1810181,
1811181,
1818181,
1860981,
1861981,
1868981,
1880881,
1881881,
1888881,
1890681,
1891681,
1898681,
1900061,
1901061,
1908061,
1910161,
1911161,
1918161,
1960961,
1961961,
1968961,
1980861,
1981861,
1988861,
1990661,
1991661,
1998661,
6000009,
6001009,
6008009,
6010109,
6011109,
6018109,
6060909,
6061909,
6068909,
6080809,
6081809,
6088809,
6090609,
6091609,
6098609,
6100019,
6101019,
6108019,
6110119,
6111119,
6118119,
6160919,
6161919,
6168919,
6180819,
6181819,
6188819,
6190619,
6191619,
6198619,
6600099,
6601099,
6608099,
6610199,
6611199,
6618199,
6660999,
6661999,
6668999,
6680899,
6681899,
6688899,
6690699,
6691699,
6698699,
6800089,
6801089,
6808089,
6810189,
6811189,
6818189,
6860989,
6861989,
6868989,
6880889,
6881889,
6888889,
6890689,
6891689,
6898689,
6900069,
6901069,
6908069,
6910169,
6911169,
6918169,
6960969,
6961969,
6968969,
6980869,
6981869,
6988869,
6990669,
6991669,
6998669,
8000008,
8001008,
8008008,
8010108,
8011108,
8018108,
8060908,
8061908,
8068908,
8080808,
8081808,
8088808,
8090608,
8091608,
8098608,
8100018,
8101018,
8108018,
8110118,
8111118,
8118118,
8160918,
8161918,
8168918,
8180818,
8181818,
8188818,
8190618,
8191618,
8198618,
8600098,
8601098,
8608098,
8610198,
8611198,
8618198,
8660998,
8661998,
8668998,
8680898,
8681898,
8688898,
8690698,
8691698,
8698698,
8800088,
8801088,
8808088,
8810188,
8811188,
8818188,
8860988,
8861988,
8868988,
8880888,
8881888,
8888888,
8890688,
8891688,
8898688,
8900068,
8901068,
8908068,
8910168,
8911168,
8918168,
8960968,
8961968,
8968968,
8980868,
8981868,
8988868,
8990668,
8991668,
8998668,
9000006,
9001006,
9008006,
9010106,
9011106,
9018106,
9060906,
9061906,
9068906,
9080806,
9081806,
9088806,
9090606,
9091606,
9098606,
9100016,
9101016,
9108016,
9110116,
9111116,
9118116,
9160916,
9161916,
9168916,
9180816,
9181816,
9188816,
9190616,
9191616,
9198616,
9600096,
9601096,
9608096,
9610196,
9611196,
9618196,
9660996,
9661996,
9668996,
9680896,
9681896,
9688896,
9690696,
9691696,
9698696,
9800086,
9801086,
9808086,
9810186,
9811186,
9818186,
9860986,
9861986,
9868986,
9880886,
9881886,
9888886,
9890686,
9891686,
9898686,
9900066,
9901066,
9908066,
9910166,
9911166,
9918166,
9960966,
9961966,
9968966,
9980866,
9981866,
9988866,
9990666,
9991666,
9998666,
10000001,
10011001,
10069001,
10088001,
10096001,
10100101,
10111101,
10169101,
10188101,
10196101,
10600901,
10611901,
10669901,
10688901,
10696901,
10800801,
10811801,
10869801,
10888801,
10896801,
10900601,
10911601,
10969601,
10988601,
10996601,
11000011,
11011011,
11069011,
11088011,
11096011,
11100111,
11111111,
11169111,
11188111,
11196111,
11600911,
11611911,
11669911,
11688911,
11696911,
11800811,
11811811,
11869811,
11888811,
11896811,
11900611,
11911611,
11969611,
11988611,
11996611,
16000091,
16011091,
16069091,
16088091,
16096091,
16100191,
16111191,
16169191,
16188191,
16196191,
16600991,
16611991,
16669991,
16688991,
16696991,
16800891,
16811891,
16869891,
16888891,
16896891,
16900691,
16911691,
16969691,
16988691,
16996691,
18000081,
18011081,
18069081,
18088081,
18096081,
18100181,
18111181,
18169181,
18188181,
18196181,
18600981,
18611981,
18669981,
18688981,
18696981,
18800881,
18811881,
18869881,
18888881,
18896881,
18900681,
18911681,
18969681,
18988681,
18996681,
19000061,
19011061.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 312498 values, from 1 to 999999986666666).
n\r | 0 | 1 |
2 | 156249 | 156249 | 2 |
3 | 104250 | 104124 | 104124 | 3 |
4 | 78126 | 93750 | 78123 | 62499 | 4 |
5 | 0 | 156249 | 0 | 78125 | 78124 | 5 |
6 | 52125 | 51999 | 51999 | 52125 | 52125 | 52125 | 6 |
7 | 53536 | 29021 | 50682 | 60408 | 30065 | 28831 | 59955 | 7 |
8 | 43754 | 50003 | 40624 | 37500 | 34372 | 43747 | 37499 | 24999 | 8 |
9 | 34538 | 34322 | 34769 | 35148 | 34821 | 34403 | 34564 | 34981 | 34952 | 9 |
10 | 0 | 78125 | 0 | 0 | 0 | 0 | 78124 | 0 | 78125 | 78124 | 10 |
11 | 39458 | 22551 | 25188 | 37453 | 21874 | 31028 | 30411 | 21494 | 36482 | 24619 | 21940 |
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.