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%I #8 May 09 2017 22:40:57
%S 1,5,6,2,5,4,24,9,3,10,11,11,19,12,34,4,42,9,13,32,11,15,18,18,5,16,
%T 27,17,17,48,19,18,56,18,55,6,61,59,37,20,12,18,18,12,65,8,28,22,7,45,
%U 34,15,55,65,75,16,24,72,23,40,13,16,19,8,16,26,24,41,13
%N Square root of smallest square formed from n by incorporating all the digits of n in a new decimal number.
%C Square root of less restrictive version of A091873: a(n) <= A091873(n).
%C First difference between a(n) and A091873(n) is for n=13. a(13) = sqrt(361) = 19, while A091873(13) = sqrt(1369) = 37.
%C If n is square then a(n) = sqrt(n).
%H Michael De Vlieger, <a href="/A286300/b286300.txt">Table of n, a(n) for n = 1..10000</a>
%e a(4) = 2 since 4 = 2^2.
%e Table of the first 20 terms of related sequences:
%e n A068165 A091873 a(n)^2 a(n)
%e 1: 1 1 1 1
%e 2: 25 5 25 5
%e 3: 36 6 36 6
%e 4: 4 2 4 2
%e 5: 25 5 25 5
%e 6: 16 4 16 4
%e 7: 576 24 576 24
%e 8: 81 9 81 9
%e 9: 9 3 9 3
%e 10: 100 10 100 10
%e 11: 121 11 121 11
%e 12: 121 11 121 11
%e 13: 1369 37 361 19
%e 14: 144 12 144 12
%e 15: 1156 34 1156 34
%e 16: 16 4 16 4
%e 17: 1764 42 1764 42
%e 18: 1089 33 81 9
%e 19: 169 13 169 13
%e 20: 2025 45 1024 32
%e ...
%t Table[If[IntegerQ@ Sqrt@ n, Sqrt@ n, k = Floor@ Sqrt@ n; Function[t, While[Function[w, Times @@ Boole@ Map[w[[#1]] >= #2 & @@ # &, #] < 1]@ DigitCount[k^2] &@ Apply[Join, Map[Lookup[t, #] /. d_ /; IntegerQ@ d :> If[d > 0, {d, #}, {10, #}] &, Keys@ t]], k++]]@ KeyDrop[PositionIndex@ DigitCount@ n, 0]; k], {n, 69}] (* _Michael De Vlieger_, May 05 2017, Version 10.1 *)
%Y Cf. A068165, A091873.
%K nonn,base,easy
%O 1,2
%A _Michael De Vlieger_, May 05 2017
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