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%I #16 Sep 08 2022 08:46:01
%S 1,3,6,16,40,100,251,631,1585,3981,10000,25119,63096,158489,398107,
%T 1000000,2511886,6309573,15848932,39810717,100000000,251188643,
%U 630957344,1584893192,3981071706,10000000000,25118864315,63095734448,158489319246,398107170553,1000000000000
%N Powers of fifth root of 100, rounded to the nearest integer.
%C The fifth root of 100, known as Pogson's ratio, is the ratio between successive stellar magnitudes.
%H Chai Wah Wu, <a href="/A205770/b205770.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PogsonsRatio.html">Pogson's Ratio</a>
%t Table[Round[100^(n/5)], {n, 0, 30}] (* _G. C. Greubel_, Jan 14 2018 *)
%o (PARI) a(n)=round(100^(n/5)) \\ _Charles R Greathouse IV_, Jan 31 2012
%o (Python)
%o from gmpy2 import iroot
%o def A205770(n):
%o m = 100**n
%o i = iroot(m,5)[0]
%o return int(i) + int(32*m >= (1+2*i)**5) # _Chai Wah Wu_, Aug 16 2016
%o (Magma) [Round(100^(n/5)): n in [0..30]]; // _G. C. Greubel_, Jan 14 2018
%Y Bisection of A018142, ratio is A189824.
%K nonn,easy
%O 0,2
%A _Franklin T. Adams-Watters_, Jan 31 2012
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