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%I #13 Aug 06 2014 16:25:20
%S 1,111111111,222222222,333333333,444444444,555555555,666666666,
%T 777777777,888888888,999999999
%N In base 10 lunar arithmetic, a(n) is the smallest number than has exactly n different square roots (or -1 if no such number exists).
%H D. Applegate, M. LeBrun and N. J. A. Sloane, <a href="http://arxiv.org/abs/1107.1130">Dismal Arithmetic</a> [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing], Journal of Integer Sequences, Vol. 14 (2011), #11.9.8.
%H <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a>
%e 1 has square root 1
%e 111111111 has 2 square roots 11011 11111
%e 222222222 has 3 square roots 22022 22122 22222
%e 333333333 has 4 square roots 33033 33133 33233 33333
%e 444444444 has 5 square roots 44044 44144 44244 44344 44444
%e 555555555 has 6 square roots 55055 55155 55255 55355 55455 55555
%e 666666666 has 7 square roots 66066 66166 66266 66366 66466 66566 66666
%e 777777777 has 8 square roots 77077 77177 77277 77377 77477 77577 77677 77777
%e 888888888 has 9 square roots 88088 88188 88288 88388 88488 88588 88688 88788 88888
%e 999999999 has 10 square roots 99099 99199 99299 99399 99499 99599 99699 99799 99899 99999
%e a(11) is presently unknown,
%Y Cf. A202082.
%K nonn,base
%O 1,2
%A _N. J. A. Sloane_, Dec 13 2011