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Trajectory of 7 under repeated application of the map n --> n + square excess of n.
2

%I #10 Mar 03 2022 12:43:49

%S 7,10,11,13,17,18,20,24,32,39,42,48,60,71,78,92,103,106,112,124,127,

%T 133,145,146,148,152,160,176,183,197,198,200,204,212,228,231,237,249,

%U 273,290,291,293,297,305,321,353,382,403,406,412,424,448,455,469,497,510,536,543

%N Trajectory of 7 under repeated application of the map n --> n + square excess of n.

%D H. Brocard, Note 2837, L'Intermédiaire des Mathématiciens, 11 (1904), p. 239.

%H S. H. Weintraub, <a href="http://www.jstor.org/stable/4145074">An interesting recursion</a>, Amer. Math. Monthly, 111 (No. 6, 2004), 528-530.

%o (PARI) lista(nn) = {print1(n=7, ", "); for (k=2, nn, m = 2*n - sqrtint(n)^2; print1(m, ", "); n = m;);} \\ _Michel Marcus_, Oct 24 2015

%Y Cf. A053186, A094761, A094763.

%K nonn

%O 0,1

%A _N. J. A. Sloane_, Jun 10 2004