A205770 Powers of fifth root of 100, rounded to the nearest integer.

1, 3, 6, 16, 40, 100, 251, 631, 1585, 3981, 10000, 25119, 63096, 158489, 398107, 1000000, 2511886, 6309573, 15848932, 39810717, 100000000, 251188643, 630957344, 1584893192, 3981071706, 10000000000, 25118864315, 63095734448, 158489319246, 398107170553, 1000000000000

Offset: 0

Author

Franklin T. Adams-Watters, Jan 31 2012

Keywords

• nonn
• easy

Comments

The fifth root of 100, known as Pogson's ratio, is the ratio between successive stellar magnitudes.

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Pogson's Ratio

Crossrefs

Bisection of A018142, ratio is A189824.

Programs

Magma

[Round(100^(n/5)): n in [0..30]]; // G. C. Greubel, Jan 14 2018

Mathematica

Table[Round[100^(n/5)], {n, 0, 30}] (* G. C. Greubel, Jan 14 2018 *)
Round[Surd[100,5]^Range[0,40]] (* Harvey P. Dale, Dec 03 2024 *)

PARI

a(n)=round(100^(n/5)) \\ Charles R Greathouse IV, Jan 31 2012

Python

from gmpy2 import iroot
def A205770(n):
    m = 100**n
    i = iroot(m,5)[0]
    return int(i) + int(32*m >= (1+2*i)**5) # Chai Wah Wu, Aug 16 2016