A197125 Numbers such that sum of digits and sum of the square of digits are both a square.

1, 4, 9, 10, 40, 90, 100, 400, 900, 1000, 1111, 1177, 1224, 1242, 1339, 1393, 1422, 1717, 1771, 1933, 2124, 2142, 2214, 2241, 2412, 2421, 3139, 3193, 3319, 3391, 3913, 3931, 4000, 4122, 4212, 4221, 4444, 4588, 4669, 4696, 4858, 4885, 4966, 5488, 5848, 5884

Offset: 1

Author

Michel Lagneau, Oct 10 2011

Keywords

• nonn
• base

Comments

The sequence contains a majority of numbers with two identical digits at least, but there exists a finite subset A = {1, 4, 9, 10, 40, 90, 156789, 156798, ..., 9876510} of 7!+6 = 5046 numbers with distinct decimal digits. The numbers > 90 of A are all permutations of 1567890.

Examples

			597618 is in the sequence because :
5+9+7+6+1+8 = 36 = 6^2 ;
5^2+9^2+7^2+6^2+1^2+8^2 = 256 = 16^2.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A028839, A175396.

Programs

Maple

for n from 1 to 6000 do:l:=evalf(floor(ilog10(n))+1):n0:=n:s1:=0:s2:=0:for m from 1 to l do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10): n0:=v :s1:=s1+u:s2:=s2+u^2: od:if sqrt(s1)=floor(sqrt(s1)) and sqrt(s2)=floor(sqrt(s2)) then printf(`%d, `, n): else fi:od:

Mathematica

sdQ[n_]:=Module[{idn=IntegerDigits[n]},IntegerQ[Sqrt[Total[idn]]] && IntegerQ[Sqrt[Total[idn^2]]]]; Select[Range[6000],sdQ] (* Harvey P. Dale, Oct 25 2011 *)

Formula

a(n) = {A028839} intersection {A175396}.