cp's OEIS Frontend

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

%I A197125 #10 Nov 21 2013 12:50:20
%S A197125 1,4,9,10,40,90,100,400,900,1000,1111,1177,1224,1242,1339,1393,1422,
%T A197125 1717,1771,1933,2124,2142,2214,2241,2412,2421,3139,3193,3319,3391,
%U A197125 3913,3931,4000,4122,4212,4221,4444,4588,4669,4696,4858,4885,4966,5488,5848,5884
%N A197125 Numbers such that  sum of  digits and sum of the square of digits are both a square.
%C A197125 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.
%H A197125 Harvey P. Dale, <a href="/A197125/b197125.txt">Table of n, a(n) for n = 1..1000</a>
%F A197125 a(n) = {A028839} intersection {A175396}.
%e A197125 597618 is in the sequence because :
%e A197125 5+9+7+6+1+8 = 36 = 6^2 ;
%e A197125 5^2+9^2+7^2+6^2+1^2+8^2 = 256 = 16^2.
%p A197125 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:
%t A197125 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 *)
%Y A197125 Cf. A028839, A175396.
%K A197125 nonn,base
%O A197125 1,2
%A A197125 _Michel Lagneau_, Oct 10 2011