cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A286300 #8 May 09 2017 22:40:57
%S A286300 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 A286300 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 A286300 34,15,55,65,75,16,24,72,23,40,13,16,19,8,16,26,24,41,13
%N A286300 Square root of smallest square formed from n by incorporating all the digits of n in a new decimal number.
%C A286300 Square root of less restrictive version of A091873: a(n) <= A091873(n).
%C A286300 First difference between a(n) and A091873(n) is for n=13. a(13) = sqrt(361) = 19, while A091873(13) = sqrt(1369) = 37.
%C A286300 If n is square then a(n) = sqrt(n).
%H A286300 Michael De Vlieger, <a href="/A286300/b286300.txt">Table of n, a(n) for n = 1..10000</a>
%e A286300 a(4) = 2 since 4 = 2^2.
%e A286300 Table of the first 20 terms of related sequences:
%e A286300    n  A068165  A091873  a(n)^2  a(n)
%e A286300    1:       1        1       1     1
%e A286300    2:      25        5      25     5
%e A286300    3:      36        6      36     6
%e A286300    4:       4        2       4     2
%e A286300    5:      25        5      25     5
%e A286300    6:      16        4      16     4
%e A286300    7:     576       24     576    24
%e A286300    8:      81        9      81     9
%e A286300    9:       9        3       9     3
%e A286300   10:     100       10     100    10
%e A286300   11:     121       11     121    11
%e A286300   12:     121       11     121    11
%e A286300   13:    1369       37     361    19
%e A286300   14:     144       12     144    12
%e A286300   15:    1156       34    1156    34
%e A286300   16:      16        4      16     4
%e A286300   17:    1764       42    1764    42
%e A286300   18:    1089       33      81     9
%e A286300   19:     169       13     169    13
%e A286300   20:    2025       45    1024    32
%e A286300 ...
%t A286300 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 A286300 Cf. A068165, A091873.
%K A286300 nonn,base,easy
%O A286300 1,2
%A A286300 _Michael De Vlieger_, May 05 2017