A153747 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.

10000, 10001, 10002, 10003, 10004, 10005, 10010, 10011, 10012, 10013, 10020, 10021, 10022, 10030, 10031, 10200, 10284, 10287, 10300, 10353, 10356, 10359, 10433, 10578, 10588, 10617, 10623, 10642, 10679, 10683, 10686, 10692, 10734

Offset: 1

Author

Doug Bell, Dec 31 2008

Keywords

• nonn
• base
• fini
• full

Comments

This sequence is a subsequence of both A153745 and A061910.

Last term is a(474) = 31493. - Giovanni Resta, Jun 06 2015

Examples

			10433^2 = 108847489; 1+0+8+8+4+7+4+8+9 = 49 = 7^2; and 108+847+489 = 1444 = 38^2.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..474 (full sequence)

Crossrefs

Cf. A061910, A153745.

Programs

Mathematica

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 *)