A153750 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.

3196200, 3330249, 3330348, 3330480, 3330801, 3331071, 3331367, 3331695, 3331731, 3331758, 3331803, 3331830, 3331860, 3331866, 3331929, 3331995, 3332025, 3332058, 3332061, 3332091, 3332124, 3332127, 3332160, 3332190

Offset

1,1

Comments

This sequence is a subsequence of both A153745 and A061910.

Last term is a(266) = 9996830. - Giovanni Resta, Jun 06 2015

Links

Giovanni Resta, Table of n, a(n) for n = 1..266 (full sequence)

Example

3331367^2 = 11098006088689;
1+1+0+9+8+0+0+6+0+8+8+6+8+9 = 64 = 8^2;
11+09+80+06+08+86+89 = 289 = 17^2;
1109800+6088689 = 7198489 = 2683^2.

Mathematica

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 *)

Crossrefs

Cf. A061910, A153745.

Sequence in context: A032783 A034638 A122034 * A234689 A232619 A223287

Adjacent sequences: A153747 A153748 A153749 * A153751 A153752 A153753

Keyword

nonn,base,fini,full

Author

Doug Bell, Dec 31 2008

Status

approved