rejected sequences
N. J. A. Sloane
njas at research.att.com
Tue May 2 06:21:55 CEST 2000
Dear Seqfan members:
Patrick de Geest submitted a bunch of sequences, which i rejected.
Below are the sequences and the reasons i rejected them.
If you think they should be included in the database, please write to me.
If enough people like them i will gladly include them.
NJAS
The sequences:
From Patrick.DeGeest at pi.be Sun Apr 30 22:34:48 2000
Hopefully you like this batch of sequences also. No doubt
they belong to the more recreational side of mathematics
but I find them nevertheless just as pleasing.
Kind regards.
Patrick
.1.
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%I A055075
%S A055075
0,302,402,403,405,507,508,602,701,702,801,802,805,901,1011,1012,1017,
%T A055075
1018,1021,1022,1024,1028,1029,1031,1035,1042,1043,1071,1101,1102,1201,
%U A055075
1202,1203,1205,1306,1308,1401,1402,1405,1505,1507,1602,1603,1605,1701
%N A055075 n, n^2 and n^3 each contains digit 0 exactly once.
%e A055075 E.g. n = 3{0}2, n^2 = 912{0}4, n^3 = 275436{0}8.
%Y A055075 Cf. A055076 up to A055084.
%K A055075 nonn,base
%O A055075 0,2
%A A055075 Patrick De Geest (Patrick.DeGeest at pi.be), May 2000.
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%I A055076
%S A055076
1,10,12,13,21,31,61,91,100,103,120,124,128,130,134,136,137,147,148,
%T A055076
159,189,210,219,301,310,415,513,514,519,591,610,621,651,661,691,716,
%U A055076
718,741,751,781,821,841,891,910,931,941,951,961,991,1000,1003,1022
%N A055076 n, n^2 and n^3 each contains digit 1 exactly once.
%e A055076 E.g. n = 7{1}8, n^2 = 5{1}5524, n^3 = 370{1}46232.
%Y A055076 Cf. A055075 up to A055084.
%K A055076 nonn,base
%O A055076 0,2
%A A055076 Patrick De Geest (Patrick.DeGeest at pi.be), May 2000.
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%I A055077
%S A055077
23,25,32,112,125,127,182,203,208,230,233,245,249,250,273,275,287,289,
%T A055077
297,302,320,323,329,352,382,425,432,452,462,521,524,528,572,623,627,
%U A055077
652,682,724,726,782,825,827,852,882,925,1012,1025,1027,1062,1092,1112
%N A055077 n, n^2 and n^3 each contains digit 2 exactly once.
%e A055076 E.g. n = 3{2}3, n^2 = 1043{2}9, n^3 = 33698{2}67.
%Y A055077 Cf. A055075 up to A055084.
%K A055077 nonn,base
%O A055077 0,1
%A A055077 Patrick De Geest (Patrick.DeGeest at pi.be), May 2000.
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%I A055078
%S A055078
37,73,153,213,305,352,354,362,369,370,389,392,473,493,503,513,523,537,
%T A055078
553,563,623,631,632,663,713,730,734,1036,1037,1113,1143,1153,1173,
%U A055078
1193,1231,1237,1238,1318,1355,1372,1387,1530,1532,1573,1623,1632,1635
%N A055078 n, n^2 and n^3 each contains digit 3 exactly once.
%e A055078 E.g. n = 157{3}, n^2 = 2474{3}29, n^3 = {3}892119517.
%Y A055078 Cf. A055075 up to A055084.
%K A055078 nonn,base
%O A055078 0,1
%A A055078 Patrick De Geest (Patrick.DeGeest at pi.be), May 2000.
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%I A055079
%S A055079
42,49,148,234,254,342,343,347,403,405,406,420,428,463,490,497,548,574,
%T A055079
584,641,647,654,684,741,748,794,842,884,946,1043,1074,1184,1194,1241,
%U A055079
1342,1343,1384,1394,1407,1423,1428,1431,1432,1437,1451,1452,1463,1472
%N A055079 n, n^2 and n^3 each contains digit 4 exactly once.
%e A055079 E.g. n = 3{4}3, n^2 = 1176{4}9, n^3 = {4}0353607.
%Y A055079 Cf. A055075 up to A055084.
%K A055079 nonn,base
%O A055079 0,1
%A A055079 Patrick De Geest (Patrick.DeGeest at pi.be), May 2000.
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%I A055080
%S A055080
5,15,35,45,50,65,85,135,145,150,165,185,195,215,245,258,265,285,305,
%T A055080
345,350,365,405,415,435,445,450,453,500,502,503,508,562,579,615,625,
%U A055080
645,650,665,685,753,759,785,850,865,895,905,915,935,945,965,1035,1045
%N A055080 n, n^2 and n^3 each contains digit 5 exactly once.
%e A055080 E.g. n = {5}79, n^2 = 33{5}241, n^3 = 194104{5}39.
%Y A055080 Cf. A055075 up to A055084.
%K A055080 nonn,base
%O A055080 0,1
%A A055080 Patrick De Geest (Patrick.DeGeest at pi.be), May 2000.
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%I A055081
%S A055081
6,16,46,60,64,76,96,106,126,136,146,160,169,176,196,206,226,269,316,
%T A055081
336,346,367,376,386,416,426,436,456,460,465,469,564,576,586,596,600,
%U A055081
602,607,613,621,622,624,625,640,644,674,675,679,682,706,756,760,896
%N A055081 n, n^2 and n^3 each contains digit 6 exactly once.
%e A055081 E.g. n = 5{6}4, n^2 = 31809{6}, n^3 = 17940{6}144.
%Y A055081 Cf. A055075 up to A055084.
%K A055081 nonn,base
%O A055081 0,1
%A A055081 Patrick De Geest (Patrick.DeGeest at pi.be), May 2000.
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%I A055082
%S A055082
137,167,273,387,473,572,637,687,724,733,755,761,792,837,857,867,873,
%T A055082
875,1037,1137,1171,1178,1272,1370,1376,1387,1407,1473,1475,1507,1572,
%U A055082
1573,1627,1670,1671,1672,1673,1723,1734,1783,1786,1876,1927,1972,1974
%N A055082 n, n^2 and n^3 each contains digit 7 exactly once.
%e A055082 E.g. n = 15{7}2, n^2 = 24{7}1184, n^3 = 3884{7}01248.
%Y A055082 Cf. A055075 up to A055084.
%K A055082 nonn,base
%O A055082 0,1
%A A055082 Patrick De Geest (Patrick.DeGeest at pi.be), May 2000.
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%I A055083
%S A055083
228,278,308,328,438,538,582,698,798,803,816,817,822,827,829,841,908,
%T A055083
1028,1087,1183,1218,1258,1278,1283,1284,1308,1368,1483,1486,1568,1628,
%U A055083
1638,1658,1685,1686,1687,1768,1785,1809,1812,1819,1866,1874,1894,1896
%N A055083 n, n^2 and n^3 each contains digit 8 exactly once.
%e A055083 E.g. n = 22{8}, n^2 = 519{8}4, n^3 = 11{8}52352.
%Y A055083 Cf. A055075 up to A055084.
%K A055083 nonn,base
%O A055083 0,1
%A A055083 Patrick De Geest (Patrick.DeGeest at pi.be), May 2000.
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%I A055084
%S A055084
139,193,198,219,297,393,439,493,509,529,589,629,769,793,891,892,913,
%T A055084
914,916,917,938,945,955,962,965,972,974,978,981,985,988,1039,1094,
%U A055084
1097,1139,1179,1219,1292,1390,1392,1394,1398,1469,1497,1693,1759,1893
%N A055084 n, n^2 and n^3 each contains digit 9 exactly once.
%e A055084 E.g. n = 3{9}3, n^2 = 15444{9}, n^3 = 606{9}8457.
%Y A055084 Cf. A055075 up to A055083.
%K A055084 nonn,base
%O A055084 0,1
%A A055084 Patrick De Geest (Patrick.DeGeest at pi.be), May 2000.
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Patrick De Geest
1. mailto:Patrick.DeGeest at pi.be (preferred)
2. mailto:Patrick.DeGeest at ping.be
Website: http://www.ping.be/~ping6758/index.shtml
ICQ# 59010931
My reply:
From njas at research.att.com Sun Apr 30 22:45:49 2000
let me try to explain why i don't want to include them:
1. they depend on the fact that we use base 10
2. they arbitrarily select the criterion of just one digit
of a particular type
(you could have said, "one even digit", or "2 odd digits", etc.)
3. they pick out n, n^2, n^3 to study
4. they were (i assume) invented by you or a correspondent. they did
not arise in trying to solve a scientific problem. You did
not come across them in trying to solve a number-theory problem,
or a chemistry problem. They are not likely to come up in any one else's work
- and that's the main reason for the existence of the database.
So (I'm sorry, i hate to reject any sequences), i'm not
going to include them.
I hope you understand my arguments, even if you don't agree with them.
All the best
Neil
PS
also, they are not very interesting! i am always willing to make an exception
to my rules if the sequence makes me laugh. those did not. forgive me!
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