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A339412 a(n) = floor(x(n)) where x(n) = (frac(x(n-1))+1)*floor(x(n-1)) and x(1) = Pi.

%I A339412 #30 Dec 05 2020 19:53:15
%S A339412 3,3,4,5,5,7,10,10,13,17,31,35,67,123,223,305,414,822,1550,2224,3273,
%T A339412 4560,7804,14372,15493,20080,40039,44226,71916,130773,183760,316165,
%U A339412 613602,1066559,1138668,1202427,2022144,2251837,2477524,4479491,7192184,11256849
%N A339412 a(n) = floor(x(n)) where x(n) = (frac(x(n-1))+1)*floor(x(n-1)) and x(1) = Pi.
%C A339412 Inspired by A249270.
%H A339412 Alois P. Heinz, <a href="/A339412/b339412.txt">Table of n, a(n) for n = 1..1000</a>
%H A339412 James Grime and Brady Haran, <a href="https://youtube.com/watch?v=_gCKX6VMvmU">2.920050977316</a>, Numberphile video, Nov 26 2020.
%p A339412 b:= proc(n) option remember; `if`(n=1, Pi,
%p A339412       (f-> (frac(f)+1)*floor(f))(b(n-1)))
%p A339412     end:
%p A339412 a:= n-> floor(b(n)):
%p A339412 seq(a(n), n=1..50);  # _Alois P. Heinz_, Dec 03 2020
%t A339412 Block[{a = {Pi}, $MaxExtraPrecision = 10^3}, Do[AppendTo[a, (FractionalPart[#] + 1) Floor[#]] &@ a[[-1]], 41]; Floor /@ a] (* _Michael De Vlieger_, Dec 04 2020 *)
%o A339412 (NARS2000) {(⌊{(⌊⍵)×1+1|⍵}⍣⍵)○1x}¨0,⍳100
%o A339412 (PARI) lista(nn) = {localprec(500); my(vx = vector(nn)); vx[1] = Pi; for (n=2, nn, vx[n] = (frac(vx[n-1])+1)*floor(vx[n-1]);); apply(floor, vx);} \\ _Michel Marcus_, Dec 03 2020
%Y A339412 Cf. A000796, A249270.
%K A339412 nonn
%O A339412 1,1
%A A339412 _Michael Turniansky_, Dec 03 2020