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

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

Author

Hieronymus Fischer, Jan 17 2006

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A085839.

Cf. A022844, A038130, A054386, A108591.

Programs

Maple

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

Mathematica

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 *)

Extensions

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