A179055 Numbers k such that the product of all numbers formed by cyclically permuting digits of k is a square.

1, 4, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 243, 324, 432, 567, 675, 756, 1000, 1010, 1020, 1030, 1040, 1050, 1060, 1070, 1080, 1090, 1111, 1212, 1313, 1414, 1515, 1616, 1717, 1818, 1919, 2000, 2010, 2020, 2030, 2040, 2050, 2060, 2070, 2080, 2090, 2121, 2222, 2323, 2424

Offset: 1

Author

Michel Lagneau, Jan 04 2011

Keywords

• nonn
• base

Examples

			756 is in the sequence because 756 * 567 * 675 = 289340100 = 17010^2.
		

Crossrefs

Cf. A061378 A062003 A061147.

Programs

Maple

with(numtheory):for n from 1 to 4000 do:pp:=1:n0:=n:l:=length(n0) :ind:=0:for
  j from 1 to l do:s:=0:for m from 1 to l do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v
  :s:=s+ u*10^m:od:s:=floor(s-u*10^l+u):n0:=s: pp:=pp*s:od:x:=sqrt(pp) :y:=floor(x):if
  x=y then printf(`%d, `, n): else fi :od:

Mathematica

cycDigitPerms[n_Integer, b_:10] := Module[{list = {n}, digits = IntegerDigits[n, b], len, counter, holder, next}, len = Length[digits]; counter = 1; While[counter < len, holder = digits[[-1]]; digits = Drop[digits, -1]; digits = Insert[digits, holder, 1]; list = Append[list, FromDigits[digits, b]]; counter++]; Return[list]]; Select[Range[2000], IntegerQ[Sqrt[Times@@cycDigitPerms[#]]] &] (* Alonso del Arte, Jan 04 2011 *)