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%I #13 Aug 10 2022 16:20:39
%S 1,3,5,17,29,29,99,169,577,985,985,3363,5741,19601,33461,33461,114243,
%T 195025,195025,1136689,1136689,3880899,6625109,6625109,38613965,
%U 38613965,131836323,225058681,225058681,768398401,1311738121,4478554083,7645370045,7645370045,26102926097
%N a(n) is the least natural number m such that the fractional part of m*(2^0.5) is less than 2^(-n).
%C Since 2^0.5 is irrational such m must exist because for any irrational number a the sequence a,2a,3a,4a,5a,... is dense modulo 1.
%C All terms are contained in A079496. - _Ralf Stephan_, Sep 09 2004
%F a(n) = min m such that m*(2^0.5)-floor(m*(2^0.5)) < 2^(-n).
%e a(7) = 99 because 99*(2^0.5) = 140.00714267... and 0.00714267... < 2^(-7) = 0.0078125 and 99 is the least natural number that satisfies this inequality.
%o (PARI) o=1:for(n=1,50, for(m=o,10^9,if(frac(sqrt(2)*m)<2^(-n),print1(m","):o=m:break)))
%Y Cf. A079496.
%K nonn
%O 1,2
%A Avi Peretz (njk(AT)netvision.net.il), Dec 25 2000
%E More terms from _Ralf Stephan_, Mar 27 2003
%E More terms from _Sean A. Irvine_, Aug 10 2022
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