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Nonnegative integers n such that the square-root of n differs from its nearest integer by less than 1/4.
4

%I #9 Jun 20 2015 17:06:26

%S 0,1,4,5,8,9,10,15,16,17,18,23,24,25,26,27,34,35,36,37,38,39,46,47,48,

%T 49,50,51,52,61,62,63,64,65,66,67,68,77,78,79,80,81,82,83,84,85,96,97,

%U 98,99,100,101,102,103,104,105,116,117,118,119,120,121,122,123,124,125

%N Nonnegative integers n such that the square-root of n differs from its nearest integer by less than 1/4.

%C The squares are a subsequence; apparently A052928(n-1) = number of terms between (n-1)^2 and n^2. - _Reinhard Zumkeller_, Jun 20 2015

%H Reinhard Zumkeller, <a href="/A128217/b128217.txt">Table of n, a(n) for n = 1..10000</a>

%t nsrQ[n_]:=Module[{sr=Sqrt[n]},Abs[First[sr-Nearest[{Floor[sr], Ceiling[sr]},sr]]]<1/4]; Select[Range[0,150],nsrQ] (* _Harvey P. Dale_, Aug 19 2011 *)

%o (Haskell)

%o a128217 n = a128217_list !! (n-1)

%o a128217_list = filter f [0..] where

%o f x = 4 * abs (root - fromIntegral (round root)) < 1

%o where root = sqrt $ fromIntegral x

%o -- _Reinhard Zumkeller_, Jun 20 2015

%Y Cf. A063656. See the first differences in A128218.

%Y Cf. A052928, A000290, A063657.

%K nonn

%O 1,3

%A _John W. Layman_, Feb 19 2007

%E Offset changed by _Reinhard Zumkeller_, Jun 20 2015