

A068515


A measure of how close the square root of 2 is to rational numbers.


0



2, 12, 12, 12, 70, 12, 70, 26, 33, 70, 25, 408, 34, 70, 70, 43, 408, 39, 146, 70, 70, 195, 49, 408, 70, 113, 147, 70, 2378, 70, 195, 126, 100, 408, 70, 408, 114, 146, 253, 93, 2378, 106, 228, 195, 125, 855, 100, 408, 165, 173, 408, 113, 1135, 147, 252, 286, 146, 2378, 135, 408
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OFFSET

1,1


COMMENTS

New peaks (in absolute terms) occur when n is a Pell number (1,2,5,12,29,70,... A000129) and take alternate Pell values with alternating signs (2,12,70,408,2378,13860,... A001542). Each new peak (after the first) appears twice (with different signs) before the next peak, when n is a numerator of a continued fraction convergent to sqrt(2) (3,7,17,41,99,... A001333) and when n is twice a Pell number (4,10,24,58,140,... A052542).


LINKS

Table of n, a(n) for n=1..60.


FORMULA

a(n) =round[1/(sqrt(2)round[sqrt(2)*n]/n)] =round[1/(sqrt(2)A022846(n)/n)] where sqrt(2)=1.41421356...


EXAMPLE

a(5) = round[1/(sqrt(2)round[sqrt(2)*5]/5)] = round[1/(sqrt(2)7/5)] = round[70.355] = 70, i.e. sqrt(2) is about 1/70 more than the nearest multiple of 1/5.


CROSSREFS

Cf. A066212.
Sequence in context: A216478 A181060 A171446 * A088240 A168457 A045895
Adjacent sequences: A068512 A068513 A068514 * A068516 A068517 A068518


KEYWORD

sign


AUTHOR

Henry Bottomley, Mar 19 2002


STATUS

approved



