A085839 -id:A085839 - cp's OEIS frontend

A134915 a(0) = 1, a(n) = floor(a(n - 1)*Pi).

1, 3, 9, 28, 87, 273, 857, 2692, 8457, 26568, 83465, 262213, 823766, 2587937, 8130243, 25541911, 80242279, 252088554, 791959549, 2488014301, 7816327450, 24555716894, 77144059797, 242355211526, 761381352089, 2391950062303, 7514532743484, 23607600862089, 74165465437218

Offset: 0

Rolf Pleisch, Jan 29 2008

nonn

Coincides with first 11 terms of A085839.

Cf. A085839, A001672.

Essentially the same as A115239.

NestList[Floor[# \[Pi]]&, 1, 30]  (* Harvey P. Dale, Mar 28 2011 *)

a(n) = A115239(n), n > 0. [From R. J. Mathar, Oct 27 2008]

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

Original entry on oeis.org

3, 9, 28, 87, 273, 857, 2692, 8457, 26568, 83465, 262213, 823766, 2587937, 8130243, 25541911, 80242279, 252088554, 791959549, 2488014301, 7816327450, 24555716894, 77144059797, 242355211526, 761381352089, 2391950062303

Offset: 1

Hieronymus Fischer, Jan 17 2006

nonn

a(n+1)/a(n) converges to Pi. Similar to sequence A085839 but with a simpler definition.

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

			a(2) = floor(a(1)*Pi) = floor(3*Pi) = 9;
a(3) = floor(a(2)*Pi) = floor(9*Pi) = 28;
a(4) = floor(a(3)*Pi) = floor(28*Pi) = 87.

G. C. Greubel, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Beatty Sequence.

Cf. A085839.

Cf. A022844, A038130, A054386, A108591.

A[1]:= 3:
for n from 2 to 50 do A[n]:= floor(Pi*A[n-1]) od:
seq(A[i],i=1..50); # Robert Israel, Feb 07 2016

a[1] = Floor[Pi]; a[n_] := a[n] = Floor[a[n - 1]*Pi]; Array[a, 25] (* Robert G. Wilson v, Jan 18 2006 *)
NestList[Floor[Pi #]&,3,30] (* Harvey P. Dale, Mar 30 2012 *)

More terms from Robert G. Wilson v, Jan 18 2006

A085421 a(0)=2, a(1)=1, a(n+2)=floor[(e-1/e)*a(n+1)+a(n-2)].

Original entry on oeis.org

2, 1, 4, 10, 27, 73, 198, 538, 1462, 3974, 10802, 29363, 79816, 216962, 589764, 1603144, 4357797, 11845720, 32200005, 87528688, 237927642, 646754385, 1758060692, 4778904432, 12990409077, 35311592938, 95986861417

Offset: 0

Gary W. Adamson, Jun 29 2003

nonn

a(n+1)/a(n) converges to e.
For n>0, floor[log a(n)] = n-1.
This resembles a Lucas sequence.

Cf. A000149, A085422, A085839.

Edited by Don Reble, Nov 14 2005

cp's OEIS Frontend

A134915 a(0) = 1, a(n) = floor(a(n - 1)*Pi).

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

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A085421 a(0)=2, a(1)=1, a(n+2)=floor[(e-1/e)*a(n+1)+a(n-2)].

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