cp's OEIS Frontend

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

%I A205770 #19 Feb 16 2025 08:33:16
%S A205770 1,3,6,16,40,100,251,631,1585,3981,10000,25119,63096,158489,398107,
%T A205770 1000000,2511886,6309573,15848932,39810717,100000000,251188643,
%U A205770 630957344,1584893192,3981071706,10000000000,25118864315,63095734448,158489319246,398107170553,1000000000000
%N A205770 Powers of fifth root of 100, rounded to the nearest integer.
%C A205770 The fifth root of 100, known as Pogson's ratio, is the ratio between successive stellar magnitudes.
%H A205770 Chai Wah Wu, <a href="/A205770/b205770.txt">Table of n, a(n) for n = 0..1000</a>
%H A205770 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PogsonsRatio.html">Pogson's Ratio</a>
%t A205770 Table[Round[100^(n/5)], {n, 0, 30}] (* _G. C. Greubel_, Jan 14 2018 *)
%t A205770 Round[Surd[100,5]^Range[0,40]] (* _Harvey P. Dale_, Dec 03 2024 *)
%o A205770 (PARI) a(n)=round(100^(n/5)) \\ _Charles R Greathouse IV_, Jan 31 2012
%o A205770 (Python)
%o A205770 from gmpy2 import iroot
%o A205770 def A205770(n):
%o A205770     m = 100**n
%o A205770     i = iroot(m,5)[0]
%o A205770     return int(i) + int(32*m >= (1+2*i)**5) # _Chai Wah Wu_, Aug 16 2016
%o A205770 (Magma) [Round(100^(n/5)): n in [0..30]]; // _G. C. Greubel_, Jan 14 2018
%Y A205770 Bisection of A018142, ratio is A189824.
%K A205770 nonn,easy
%O A205770 0,2
%A A205770 _Franklin T. Adams-Watters_, Jan 31 2012