A202174 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).

1, 111111111, 222222222, 333333333, 444444444, 555555555, 666666666, 777777777, 888888888, 999999999

Offset

1,2

Links

Table of n, a(n) for n=1..10.

D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [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.

Index entries for sequences related to dismal (or lunar) arithmetic

Example

1 has square root 1
111111111 has 2 square roots 11011 11111
222222222 has 3 square roots 22022 22122 22222
333333333 has 4 square roots 33033 33133 33233 33333
444444444 has 5 square roots 44044 44144 44244 44344 44444
555555555 has 6 square roots 55055 55155 55255 55355 55455 55555
666666666 has 7 square roots 66066 66166 66266 66366 66466 66566 66666
777777777 has 8 square roots 77077 77177 77277 77377 77477 77577 77677 77777
888888888 has 9 square roots 88088 88188 88288 88388 88488 88588 88688 88788 88888
999999999 has 10 square roots 99099 99199 99299 99399 99499 99599 99699 99799 99899 99999
a(11) is presently unknown,

Crossrefs

Cf. A202082.

Sequence in context: A293973 A094327 A180513 * A172525 A038451 A202082

Adjacent sequences: A202171 A202172 A202173 * A202175 A202176 A202177

Keyword

nonn,base

Author

N. J. A. Sloane, Dec 13 2011

Status

approved