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A115239 a(1) = floor(Pi) = 3; a(n+1) = floor(a(n)*Pi).

%I A115239 #22 Feb 16 2025 08:33:00
%S A115239 3,9,28,87,273,857,2692,8457,26568,83465,262213,823766,2587937,
%T A115239 8130243,25541911,80242279,252088554,791959549,2488014301,7816327450,
%U A115239 24555716894,77144059797,242355211526,761381352089,2391950062303
%N A115239 a(1) = floor(Pi) = 3; a(n+1) = floor(a(n)*Pi).
%C A115239 a(n+1)/a(n) converges to Pi. Similar to sequence A085839 but with a simpler definition.
%C A115239 Subset of the Beatty sequence of Pi = A022844 = floor(n*Pi). Primes in this sequence include a(1) = 3, a(6) = 857, a(15) = 25541911. - _Jonathan Vos Post_, Jan 18 2006
%H A115239 G. C. Greubel, <a href="/A115239/b115239.txt">Table of n, a(n) for n = 1..1000</a>
%H A115239 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence</a>.
%e A115239 a(2) = floor(a(1)*Pi) = floor(3*Pi) = 9;
%e A115239 a(3) = floor(a(2)*Pi) = floor(9*Pi) = 28;
%e A115239 a(4) = floor(a(3)*Pi) = floor(28*Pi) = 87.
%p A115239 A[1]:= 3:
%p A115239 for n from 2 to 50 do A[n]:= floor(Pi*A[n-1]) od:
%p A115239 seq(A[i],i=1..50); # _Robert Israel_, Feb 07 2016
%t A115239 a[1] = Floor[Pi]; a[n_] := a[n] = Floor[a[n - 1]*Pi]; Array[a, 25] (* _Robert G. Wilson v_, Jan 18 2006 *)
%t A115239 NestList[Floor[Pi #]&,3,30] (* _Harvey P. Dale_, Mar 30 2012 *)
%Y A115239 Cf. A085839.
%Y A115239 Cf. A022844, A038130, A054386, A108591.
%K A115239 nonn
%O A115239 1,1
%A A115239 _Hieronymus Fischer_, Jan 17 2006
%E A115239 More terms from _Robert G. Wilson v_, Jan 18 2006