A017919 Powers of sqrt(5) rounded down.

1, 2, 5, 11, 25, 55, 125, 279, 625, 1397, 3125, 6987, 15625, 34938, 78125, 174692, 390625, 873464, 1953125, 4367320, 9765625, 21836601, 48828125, 109183006, 244140625, 545915033, 1220703125, 2729575167

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

a(n) is the total length (rounded down to integer) of the elements of a variant of a 5-element fractal after n iterations, starting with 5 elements, each of whose length is 1/5 (in some units). See illustration in the Links. - Kival Ngaokrajang, Feb 26 2015

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Kival Ngaokrajang, Illustration of initial terms

Crossrefs

Cf. A017920, A017921.

Programs

Magma

[Floor(Sqrt(5^n)): n in [0..40]]; // Vincenzo Librandi, Nov 20 2011

Mathematica

Floor[(Sqrt[5])^Range[0,40]] (* Vincenzo Librandi, Nov 20 2011 *)

PARI

a(n)=sqrtint(5^n) \\ Charles R Greathouse IV, Nov 18 2011

Python

from math import isqrt
def A017919(n): return isqrt(5**n) # Chai Wah Wu, Jun 19 2024