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%I #3 Mar 30 2012 18:51:35
%S 2,-12,12,-12,70,12,-70,26,-33,70,-25,-408,34,-70,70,-43,408,39,-146,
%T 70,-70,195,-49,-408,70,-113,147,-70,2378,70,-195,126,-100,408,70,
%U -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
%N A measure of how close the square root of 2 is to rational numbers.
%C 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).
%F a(n) =round[1/(sqrt(2)-round[sqrt(2)*n]/n)] =round[1/(sqrt(2)-A022846(n)/n)] where sqrt(2)=1.41421356...
%e 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.
%Y Cf. A066212.
%K sign
%O 1,1
%A _Henry Bottomley_, Mar 19 2002
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