%I #27 Jul 23 2023 01:53:18

%S 3,5,8,12,15,16,21,24,27,32,35,40,45,48,55,60,63,65,72,77,80,84,91,96,

%T 99,105,112,117,120,128,135,140,143,144,153,160,165,168,171,180,187,

%U 192,195,200,209,216,221,224,231,240,247,252,255,264,273,280,285

%N Positive numbers differing from next greater square by a square.

%C Square terms in the sequence are 16, 144, 576, 1600, 3600, 7056, ..., that is, A060300 ((2n(n+1))^2) except 0. And their indices, ind(n), are: 6, 34, 100, 220, 410, 686, ..., that is, ind(n) = 2*A132124(.). - _Michel Marcus_, suggested by _Zak Seidov_, Nov 26 2013

%H Zak Seidov, <a href="/A218485/b218485.txt">Table of n, a(n) for n = 1..1515</a> (all terms up to 20000)

%H E. J. Barbeau, <a href="http://dx.doi.org/10.4153/CMB-1985-040-9">Numbers differing from consecutive squares by squares</a>, Canad. Math. Bull. 28(1985), pp. 337-342.

%e 8 = 3^2 - 1^2.

%t Select[Range[300],IntegerQ[Sqrt[(1+Floor[Sqrt[#]])^2-#]]&] (* _Zak Seidov_, Nov 26 2013 *)

%o (PARI) sq1(n) = {for (i=1, n, a = sqrtint(i) + 1; if (issquare(a^2-i), print1(i, ", ")););}

%Y Cf. A060300, A218486, A218487, A218488.

%K nonn

%O 1,1

%A _Michel Marcus_, Oct 30 2012