A242077 Numbers k such that no final group of decimal digits of k^2 less than the total forms a square.

4, 5, 6, 14, 16, 24, 26, 34, 36, 64, 66, 74, 76, 84, 86, 114, 116, 124, 126, 134, 136, 164, 166, 174, 176, 184, 186, 214, 216, 224, 226, 234, 236, 264, 266, 274, 276, 284, 286, 314, 316, 324, 326, 334, 336, 364, 366, 374, 376, 384, 386, 414, 416, 424, 426, 434

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000.

Formula

a(n) = sqrt(A192689(n)).

Example

34 is in the sequence because 34^2 = 1156 but neither 156, 56 nor 6 are perfect squares.
36 is in the sequence because 36^2 = 1296 but neither 296, 96 nor 6 are perfect squares.
44 is not in the sequence because 44^2 = 1936 and 36 = 6^2.

Mathematica

nfgsQ[n_]:=Module[{s=n^2}, NoneTrue[FromDigits/@Rest[NestList[ Rest, IntegerDigits[ s], IntegerLength[ s]-1]], IntegerQ[Sqrt[#]]&]]; Select[ Range[ 4, 500], nfgsQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 18 2019 *)

Crossrefs

Cf. A192689.

Sequence in context: A139061 A029645 A191208 * A050162 A345972 A224678

Adjacent sequences: A242074 A242075 A242076 * A242078 A242079 A242080

Keyword

nonn,base

Author

J. Lowell, May 03 2014

Status

approved