This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A219960 #13 Sep 14 2013 17:30:40 %S A219960 366,680,691,1026,1136,1298,1323,1417,1464,1583,1604,1702,2079,2125, %T A219960 2222,2223,2374,2507,2604,2627,2821,2844,2897,3152,3157,3159,3183, %U A219960 3210,3231,3459,3697,3715,3762,3802,3866,3888,3936,3948,4004,4111,4133,4145,4231,4299 %N A219960 Numbers which do not reach zero under the repeated iteration x -> ceiling(sqrt(x)) * (ceiling(sqrt(x))^2 - x). %C A219960 Ceiling equivalent of A219303, with somewhat different behavior despite a near-identical iterative process. %C A219960 Conjecture #1: All numbers under the iteration reach 0 or, like the elements of this sequence, reach a finite loop, and none expand indefinitely to infinity. %C A219960 Conjecture #2: There are an infinite number of such finite loops, though there is often significant distance between them. %C A219960 Conjecture #3: There are an infinite number of pairs of consecutive integers in this sequence despite being less abundant than in A219303. %H A219960 Carl R. White, <a href="/A219960/b219960.txt">Table of n, a(n) for n = 1..10000</a> %e A219960 1702 is in this list as 38 iterations return to 1702. Many other numbers reach this loop. 5832 is also in this list and is the smallest member of a different loop. %e A219960 1703 is _not_ in this list because the iteration runs: 1703 -> 2562 -> 1989 -> 1620 -> 2501 -> 5100 -> 6048 -> 2808 -> 53 -> 88 -> 120 -> 11 -> 20 -> 25 -> 0. %t A219960 f[n_] := Ceiling[Sqrt[n]]*(Ceiling[Sqrt[n]]^2 - n); Select[Range[5000], NestWhileList[f, #, UnsameQ, All][[-1]] > 0 &] (* _T. D. Noe_, Dec 04 2012 *) %Y A219960 Cf. A219303, A219961, A219962, A219963 %K A219960 nonn %O A219960 1,1 %A A219960 _Carl R. White_, Dec 02 2012