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

1,1

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Beatty Sequence.

Example

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.

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 *)

Crossrefs

Cf. A085839.

Cf. A022844, A038130, A054386, A108591.

Sequence in context: A052939 A225114 A085839 * A134915 A339064 A118365

Adjacent sequences: A115236 A115237 A115238 * A115240 A115241 A115242

Keyword

nonn

Author

Hieronymus Fischer, Jan 17 2006

Extensions

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

Status

approved