A339412 a(n) = floor(x(n)) where x(n) = (frac(x(n-1))+1)*floor(x(n-1)) and x(1) = Pi.

3, 3, 4, 5, 5, 7, 10, 10, 13, 17, 31, 35, 67, 123, 223, 305, 414, 822, 1550, 2224, 3273, 4560, 7804, 14372, 15493, 20080, 40039, 44226, 71916, 130773, 183760, 316165, 613602, 1066559, 1138668, 1202427, 2022144, 2251837, 2477524, 4479491, 7192184, 11256849

Offset

1,1

Comments

Inspired by A249270.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

James Grime and Brady Haran, 2.920050977316, Numberphile video, Nov 26 2020.

Maple

b:= proc(n) option remember; `if`(n=1, Pi,
      (f-> (frac(f)+1)*floor(f))(b(n-1)))
    end:
a:= n-> floor(b(n)):
seq(a(n), n=1..50);  # Alois P. Heinz, Dec 03 2020

Mathematica

Block[{a = {Pi}, $MaxExtraPrecision = 10^3}, Do[AppendTo[a, (FractionalPart[#] + 1) Floor[#]] &@ a[[-1]], 41]; Floor /@ a] (* Michael De Vlieger, Dec 04 2020 *)

Prog

(NARS2000) {(⌊{(⌊⍵)×1+1|⍵}⍣⍵)○1x}¨0, ⍳100
(PARI) lista(nn) = {localprec(500); my(vx = vector(nn)); vx[1] = Pi; for (n=2, nn, vx[n] = (frac(vx[n-1])+1)*floor(vx[n-1]); ); apply(floor, vx); } \\ Michel Marcus, Dec 03 2020

Crossrefs

Cf. A000796, A249270.

Sequence in context: A274004 A196592 A120180 * A279400 A063197 A327226

Adjacent sequences: A339409 A339410 A339411 * A339413 A339414 A339415

Keyword

nonn

Author

Michael Turniansky, Dec 03 2020

Status

approved