A258911 a(1)=a(2)=1, a(n) = ceiling(Pi*a(n-1) - a(n-2)), n>2.

1, 1, 3, 9, 26, 73, 204, 568, 1581, 4399, 12239, 34051, 94736, 263571, 733297, 2040150, 5676024, 15791606, 43934770, 122233545, 340073237, 946138039, 2632307076, 7323498533, 20375142114, 56686898249, 157712000980

Offset

1,3

Comments

Ratio of consecutive terms approaches (Pi + sqrt(Pi^2 - 4))/2, or approximately 2.782159649779516149316 (A189039).

Links

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

Example

a(3) = ceiling(Pi*1 - 1) = 3;
a(4) = ceiling(Pi*3 - 1) = 9;
a(5) = ceiling(Pi*9 - 3) = 26.

Mathematica

RecurrenceTable[{a[n] == Ceiling[Pi*a[n - 1] - a[n - 2]], a[1] == 1,
  a[2] == 1}, a, {n, 1, 50}] (* G. C. Greubel, Jun 03 2017 *)
nxt[{a_, b_}]:={b, Ceiling[b*Pi-a]}; NestList[nxt, {1, 1}, 30][[All, 1]] (* Harvey P. Dale, Apr 02 2020 *)

Prog

(Magma) I:=[1, 1]; [n le 2 select I[n] else Ceiling(pi*Self(n-1)-Self(n-2)): n in [1..200]];
(PARI)  main(size)={my(v=vector(size), i); v[1]=1; v[2]=1; for(i=3, size, v[i]=ceil(Pi*v[i-1]-v[i-2])); return(v); } /* Anders Hellström, Jul 14 2015 */

Crossrefs

Cf. A189039.

Sequence in context: A054447 A061667 A234270 * A268093 A127911 A116423

Adjacent sequences: A258908 A258909 A258910 * A258912 A258913 A258914

Keyword

nonn

Author

Morris Neene, Jun 14 2015

Status

approved