A085421 -id:A085421 - cp's OEIS frontend

A085839 a(0)=1, a(1)=3, a(n) = floor((Pi + 1/Pi)*a(n-1) - a(n-2)).

1, 3, 9, 28, 87, 273, 857, 2692, 8457, 26568, 83465, 262212, 823762, 2587924, 8130202, 25541782, 80241874, 252087281, 791955549, 2488001734, 7816287969, 24555592861, 77143670136, 242353987370, 761377506289, 2391937980365

Offset: 0

Gary W. Adamson, Jul 05 2003

nonn

a(n+1)/a(n) converges to Pi.

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Cf. A000796, A085421, A085422.

a[n_] := a[n] = Floor[(Pi + 1/Pi)a[n - 1] - a[n - 2]]; Table[a[n], {n, 0, 25}] (* Robert G. Wilson v *)
nxt[{a_,b_}]:=Module[{c=Pi+1/Pi},{b,Floor[b*c-a]}]; NestList[nxt,{1,3},30][[All,1]] (* Harvey P. Dale, Oct 07 2018 *)

Edited by Don Reble, Nov 14 2005

Definition corrected by Robert G. Wilson v, Apr 26 2006

A085560 a(0) = 1, then (for n>0) a(n) = floor[(e + 1/e)*a(n-1) - a(n-2)].

Original entry on oeis.org

1, 3, 8, 21, 56, 151, 410, 1114, 3027, 8227, 22362, 60785, 165230, 449141, 1220891, 3318725, 9021229, 24522242, 66658364, 181196219, 492542389, 1338869025, 3639423341, 9892978333, 26891903231, 73099771885, 198705781579

Offset: 0

Gary W. Adamson, Jul 05 2003

nonn

A recursive series with [a(n+1)/a(n)] converging to e.

a(15)/a(14) = 3318725/1220891 = 2.71828115... floor[log a(n)] = n. Example: log a(15) = log 3318725 = 15.01509...; floor(15.015...) = 15.

			a(5) = 151 = floor[(e + 1/e)*a(4) - a(3)] = floor[(e + 1/e)(56) - 21].

Cf. A085421.

a[0] = 1; a[1] = 3; a[n_] := a[n] = Floor[(E + 1/E)*a[n - 1] - a[n - 2]]; Table[ a[n], {n, 0, 27}]

More terms from Robert G. Wilson v, Jul 13 2003

cp's OEIS Frontend

A085839 a(0)=1, a(1)=3, a(n) = floor((Pi + 1/Pi)*a(n-1) - a(n-2)).

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