A017968 Powers of sqrt(21) rounded to nearest integer.

1, 5, 21, 96, 441, 2021, 9261, 42439, 194481, 891224, 4084101, 18715702, 85766121, 393029742, 1801088541, 8253624572, 37822859361, 173326116021, 794280046581, 3639848436450, 16679880978201, 76436817165460, 350277500542221, 1605173160474663, 7355827511386641

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Maple

a:= n-> round(sqrt(21)^n):
seq(a(n), n=0..25);  # Alois P. Heinz, Jul 29 2022

Mathematica

Floor[(Sqrt[21])^Range[0, 25]+1/2] (* Harvey P. Dale, Sep 22 2011 *)

Prog

(PARI) a(n)=round(sqrt(21)^n) \\ Charles R Greathouse IV, Nov 18 2011
(Magma) [Round(Sqrt(21)^n): n in [0..30]]; // Vincenzo Librandi, Nov 20 2011
(Python)
from math import isqrt
def A017968(n): return (m:=isqrt(k:=21**n))+int((k-m*(m+1)<<2)>=1) # Chai Wah Wu, Jul 29 2022

Crossrefs

Cf. A010477 (sqrt(21)), A017967.

Bisection gives A009965 (even part).

Sequence in context: A343349 A159289 A201869 * A017969 A050897 A338673

Adjacent sequences: A017965 A017966 A017967 * A017969 A017970 A017971

Keyword

nonn

Author

N. J. A. Sloane

Status

approved