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

0,2

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

Mathematica

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

Prog

(PARI) a(n)=sqrtint(5^n) \\ Charles R Greathouse IV, Nov 18 2011
(Magma) [Floor(Sqrt(5^n)): n in [0..40]]; // Vincenzo Librandi, Nov 20 2011
(Python)
from math import isqrt
def A017919(n): return isqrt(5**n) # Chai Wah Wu, Jun 19 2024

Crossrefs

Cf. A017920, A017921.

Sequence in context: A151529 A192922 A215091 * A017920 A228765 A006054

Adjacent sequences: A017916 A017917 A017918 * A017920 A017921 A017922

Keyword

nonn

Author

N. J. A. Sloane

Status

approved