%I #22 May 09 2021 19:21:57
%S 10000,10001,10002,10003,10004,10005,10010,10011,10012,10013,10020,
%T 10021,10022,10030,10031,10200,10284,10287,10300,10353,10356,10359,
%U 10433,10578,10588,10617,10623,10642,10679,10683,10686,10692,10734
%N Numbers k such that there are 9 digits in k^2 and for each factor f of 9 (1,3) the sum of digit groupings of size f is a square.
%C This sequence is a subsequence of both A153745 and A061910.
%C Last term is a(474) = 31493. - _Giovanni Resta_, Jun 06 2015
%H Giovanni Resta, <a href="/A153747/b153747.txt">Table of n, a(n) for n = 1..474</a> (full sequence)
%e 10433^2 = 108847489; 1+0+8+8+4+7+4+8+9 = 49 = 7^2; and 108+847+489 = 1444 = 38^2.
%t dgfsQ[n_]:=Module[{idn2=IntegerDigits[n^2]},AllTrue[{Sqrt[ Total[ idn2]], Sqrt[ Total[ FromDigits/@ Partition[idn2,3]]]},IntegerQ]]; Select[ Range[ 10000,31622],dgfsQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Sep 19 2018 *)
%Y Cf. A061910, A153745.
%K nonn,base,fini,full
%O 1,1
%A _Doug Bell_, Dec 31 2008