cp's OEIS Frontend

A058580 a(n) is the least natural number m such that the fractional part of m*(2^0.5) is less than 2^(-n).

%I A058580 #13 Aug 10 2022 16:20:39
%S A058580 1,3,5,17,29,29,99,169,577,985,985,3363,5741,19601,33461,33461,114243,
%T A058580 195025,195025,1136689,1136689,3880899,6625109,6625109,38613965,
%U A058580 38613965,131836323,225058681,225058681,768398401,1311738121,4478554083,7645370045,7645370045,26102926097
%N A058580 a(n) is the least natural number m such that the fractional part of m*(2^0.5) is less than 2^(-n).
%C A058580 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 A058580 All terms are contained in A079496. - _Ralf Stephan_, Sep 09 2004
%F A058580 a(n) = min m such that m*(2^0.5)-floor(m*(2^0.5)) < 2^(-n).
%e A058580 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 A058580 (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 A058580 Cf. A079496.
%K A058580 nonn
%O A058580 1,2
%A A058580 Avi Peretz (njk(AT)netvision.net.il), Dec 25 2000
%E A058580 More terms from _Ralf Stephan_, Mar 27 2003
%E A058580 More terms from _Sean A. Irvine_, Aug 10 2022