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a(0)=209; for n > 0, a(n) = a(n-1) + floor(sqrt(a(n-1))).
1

%I #22 Dec 26 2023 12:24:08

%S 209,223,237,252,267,283,299,316,333,351,369,388,407,427,447,468,489,

%T 511,533,556,579,603,627,652,677,703,729,756,783,810,838,866,895,924,

%U 954,984,1015,1046,1078,1110,1143,1176,1210,1244,1279,1314,1350,1386

%N a(0)=209; for n > 0, a(n) = a(n-1) + floor(sqrt(a(n-1))).

%C Row 13 in square array A159016. This sequence contains infinitely many squares.

%C The squares in the sequence are (A175806(k))^2, k = 0,1,2,... [_Vincenzo Librandi_, Dec 05 2010]

%t NestList[#+Floor[Sqrt[#]]&,209,50] (* _Harvey P. Dale_, Jun 12 2017 *)

%o (Magma) [n eq 1 select 209 else Self(n-1)+Floor(Sqrt (Self(n-1))):n in [1..30]]; // _Marius A. Burtea_, Jan 07 2020

%Y Cf. A159016, A175806.

%K nonn

%O 0,1

%A _Philippe Deléham_, Apr 07 2009