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

1,2

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

Links

Table of n, a(n) for n=1..35.

Formula

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

Example

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.

Prog

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

Crossrefs

Cf. A079496.

Sequence in context: A193070 A030077 A352568 * A161682 A079373 A181291

Adjacent sequences: A058577 A058578 A058579 * A058581 A058582 A058583

Keyword

nonn

Author

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

Extensions

More terms from Ralf Stephan, Mar 27 2003

More terms from Sean A. Irvine, Aug 10 2022

Status

approved