A318053 a(n) = ceiling(sqrt(2*a(n-1)*a(n-2))), a(1) = a(2) = 1.

1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 15, 19, 24, 31, 39, 50, 63, 80, 101, 128, 161, 204, 257, 324, 409, 515, 650, 819, 1032, 1301, 1639, 2066, 2603, 3280, 4133, 5207, 6561, 8266, 10415, 13122, 16533, 20831, 26245, 33067, 41662, 52491, 66135, 83325

Offset

1,3

Comments

a(n)/a(n-1) ~ cube root of 2.

a(n)/a(n-3) ~ 2.

Links

Table of n, a(n) for n=1..48.

Example

a(12) = ceiling(sqrt(2*a(11)*a(10))) = ceiling(sqrt(2*15*12)) = ceiling(sqrt(360)) = 19.

Mathematica

a[n_] := a[n] = If[n<3, 1, Ceiling[Sqrt[2 a[n-1] a[n-2]]]]; Array[a, 50] (* Giovanni Resta, Nov 26 2019 *)
RecurrenceTable[{a[1]==a[2]==1, a[n]==Ceiling[Sqrt[2a[n-1]a[n-2]]]}, a, {n, 50}] (* Harvey P. Dale, Apr 13 2020 *)

Prog

(Python)
import math
r = []
r.append(1)
r.append(1)
i = 2
while i < 1001:
  r.append(math.ceil(math.sqrt(2*r[i-1]*r[i-2])))
  i += 1
print(r)

Crossrefs

Cf. A017981.

Sequence in context: A364159 A280200 A052336 * A061287 A225500 A064651

Adjacent sequences: A318050 A318051 A318052 * A318054 A318055 A318056

Keyword

nonn

Author

Oren Meisner, Aug 14 2018

Status

approved