A153752 Numbers k such that there are 16 digits in k^2 and for each factor f of 16 (1,2,4,8) the sum of digit groupings of size f is a square.

31883334, 31886667, 31956690, 31970049, 32469999, 33338100, 33341067, 33870000, 34140000, 34149999, 34713042, 34763334, 34856667, 35780000, 36356249, 36356480, 36359065, 37523635, 37737452, 37949451, 38362409

Offset

1,1

Comments

This sequence is a subsequence of both A153745 and A061910.

This sequence contains 124 terms, with a(124) = 9998956. - Giovanni Resta, Jun 06 2015

Links

Giovanni Resta, Table of n, a(n) for n = 1..124 (all terms)

Example

31883334^2 = 1016546986955556;
1+0+1+6+5+4+6+9+8+6+9+5+5+5+5+6 = 81 = 9^2;
10+16+54+69+86+95+55+56 = 441 = 21^2;
1016+5469+8695+5556 = 20736 = 144^2;
10165469+86955556 = 97121025 = 9855^2.

Mathematica

okQ[n_]:=Module[{n2=IntegerDigits[n^2]}, And@@(IntegerQ[Sqrt[ #]]&/@ (Total/@(Table[ FromDigits/@Partition[n2, 2^i], {i, 0, 3}])))]; Select[ Range[31622777, 38400000], okQ] (* Harvey P. Dale, Aug 12 2012 *)

Crossrefs

Cf. A004159, A061910, A153745.

Sequence in context: A151621 A052097 A252356 * A209912 A290264 A206043

Adjacent sequences: A153749 A153750 A153751 * A153753 A153754 A153755

Keyword

nonn,base,fini,full

Author

Doug Bell, Dec 31 2008

Status

approved