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

1, 3, 5, 17, 29, 29, 99, 169, 577, 985, 985, 3363, 5741, 19601, 33461, 33461, 114243, 195025, 195025, 1136689, 1136689, 3880899, 6625109, 6625109, 38613965, 38613965, 131836323, 225058681, 225058681, 768398401, 1311738121, 4478554083, 7645370045, 7645370045, 26102926097

Offset: 1

Author

Avi Peretz (njk(AT)netvision.net.il), Dec 25 2000

Keywords

• nonn

Comments

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.

All terms are contained in A079496. - Ralf Stephan, Sep 09 2004

Examples

			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.
		

Crossrefs

Cf. A079496.

Programs

PARI

o=1:for(n=1,50, for(m=o,10^9,if(frac(sqrt(2)*m)<2^(-n),print1(m","):o=m:break)))

Formula

a(n) = min m such that m*(2^0.5)-floor(m*(2^0.5)) < 2^(-n).

Extensions

More terms from Ralf Stephan, Mar 27 2003

More terms from Sean A. Irvine, Aug 10 2022