Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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