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

%I #33 Mar 17 2022 05:51:34

%S 4,5,6,14,16,24,26,34,36,64,66,74,76,84,86,114,116,124,126,134,136,

%T 164,166,174,176,184,186,214,216,224,226,234,236,264,266,274,276,284,

%U 286,314,316,324,326,334,336,364,366,374,376,384,386,414,416,424,426,434

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

%H Harvey P. Dale, <a href="/A242077/b242077.txt">Table of n, a(n) for n = 1..1000</a>.

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

%e 34 is in the sequence because 34^2 = 1156 but neither 156, 56 nor 6 are perfect squares.

%e 36 is in the sequence because 36^2 = 1296 but neither 296, 96 nor 6 are perfect squares.

%e 44 is not in the sequence because 44^2 = 1936 and 36 = 6^2.

%t 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 *)

%Y Cf. A192689.

%K nonn,base

%O 1,1

%A _J. Lowell_, May 03 2014