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Numbers k such that there are 14 digits in k^2 and for each factor f of 14 (1,2,7) the sum of digit groupings of size f is a square.
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%I #23 May 09 2021 07:53:10

%S 3196200,3330249,3330348,3330480,3330801,3331071,3331367,3331695,

%T 3331731,3331758,3331803,3331830,3331860,3331866,3331929,3331995,

%U 3332025,3332058,3332061,3332091,3332124,3332127,3332160,3332190

%N Numbers k such that there are 14 digits in k^2 and for each factor f of 14 (1,2,7) 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(266) = 9996830. - _Giovanni Resta_, Jun 06 2015

%H Giovanni Resta, <a href="/A153750/b153750.txt">Table of n, a(n) for n = 1..266</a> (full sequence)

%e 3331367^2 = 11098006088689;

%e 1+1+0+9+8+0+0+6+0+8+8+6+8+9 = 64 = 8^2;

%e 11+09+80+06+08+86+89 = 289 = 17^2;

%e 1109800+6088689 = 7198489 = 2683^2.

%t sdgQ[n_]:=Module[{idn=IntegerDigits[n^2],t2,t7},t2=Total[FromDigits/@ Partition[ idn,2]];t7=Total[FromDigits/@Partition[idn,7]]; AllTrue[ {Sqrt[Total[idn]],Sqrt[t2],Sqrt[t7]},IntegerQ]]; Select[Range[ Round[ 3.16*10^6],Round[3.34*10^6]],sdgQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Aug 07 2016 *)

%Y Cf. A061910, A153745.

%K nonn,base,fini,full

%O 1,1

%A _Doug Bell_, Dec 31 2008