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A286300 Square root of smallest square formed from n by incorporating all the digits of n in a new decimal number. 1
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, 27, 17, 17, 48, 19, 18, 56, 18, 55, 6, 61, 59, 37, 20, 12, 18, 18, 12, 65, 8, 28, 22, 7, 45, 34, 15, 55, 65, 75, 16, 24, 72, 23, 40, 13, 16, 19, 8, 16, 26, 24, 41, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Square root of less restrictive version of A091873: a(n) <= A091873(n).

First difference between a(n) and A091873(n) is for n=13. a(13) = sqrt(361) = 19, while A091873(13) = sqrt(1369) = 37.

If n is square then a(n) = sqrt(n).

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

EXAMPLE

a(4) = 2 since 4 = 2^2.

Table of the first 20 terms of related sequences:

   n  A068165  A091873  a(n)^2  a(n)

   1:       1        1       1     1

   2:      25        5      25     5

   3:      36        6      36     6

   4:       4        2       4     2

   5:      25        5      25     5

   6:      16        4      16     4

   7:     576       24     576    24

   8:      81        9      81     9

   9:       9        3       9     3

  10:     100       10     100    10

  11:     121       11     121    11

  12:     121       11     121    11

  13:    1369       37     361    19

  14:     144       12     144    12

  15:    1156       34    1156    34

  16:      16        4      16     4

  17:    1764       42    1764    42

  18:    1089       33      81     9

  19:     169       13     169    13

  20:    2025       45    1024    32

...

MATHEMATICA

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 *)

CROSSREFS

Cf. A068165, A091873.

Sequence in context: A211394 A060011 A021068 * A091873 A038690 A154801

Adjacent sequences:  A286297 A286298 A286299 * A286301 A286302 A286303

KEYWORD

nonn,base,easy

AUTHOR

Michael De Vlieger, May 05 2017

STATUS

approved

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Last modified April 11 14:58 EDT 2021. Contains 342886 sequences. (Running on oeis4.)