

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



1, 3, 5, 17, 29, 29, 99, 169, 577, 985, 985, 3363, 5741, 19601, 33461, 33461, 114243, 195025, 195025, 1136689, 1136689
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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..21.


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

Sequence in context: A193066 A193070 A030077 * 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


STATUS

approved



