A286300 Square root of smallest square formed from n by incorporating all the digits of n in a new decimal number.

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

Offset: 1

Author

Michael De Vlieger, May 05 2017

Keywords

• nonn
• base
• easy

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).

Examples

			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
...
		

Links

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

Crossrefs

Cf. A068165, A091873.

Programs

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 *)