%I #24 Apr 11 2023 11:19:33
%S 10000000,10000001,10000002,10000003,10000004,10000005,10000010,
%T 10000011,10000012,10000013,10000020,10000021,10000022,10000030,
%U 10000031,10000200,10000300,10011003,10022000,10035990,10042440
%N Numbers k such that there are 15 digits in k^2 and for each factor f of 15 (1,3,5) the sum of digit groupings of size f is a square.
%C This sequence is a subsequence of both A153745 and A061910.
%C The last term is a(2782) = 31616301. - _Giovanni Resta_, Jun 06 2015
%H Giovanni Resta, <a href="/A153751/b153751.txt">Table of n, a(n) for n = 1..2782</a> (all terms)
%e 10000011^2 = 100000220000121;
%e 1+0+0+0+0+0+2+2+0+0+0+0+1+2+1 = 9 = 3^2;
%e 100+000+220+000+121 = 441 = 21^2;
%e 10000+02200+00121 = 12321 = 111^2.
%t Select[Range[10^7,31622776],AllTrue[{Sqrt[Total[IntegerDigits[#^2]]],Sqrt[Total[ FromDigits/@ Partition[IntegerDigits[#^2],3]]],Sqrt[Total[FromDigits/@Partition[IntegerDigits[#^2],5]]]},IntegerQ]&] (* _Harvey P. Dale_, Apr 11 2023 *)
%Y Cf. A004159, A061910, A153745.
%K nonn,base,fini,full
%O 1,1
%A _Doug Bell_, Dec 31 2008